Study Centre

আপনার কাছে যদি মনে হয় প্রশ্নটি অধ্যায় অনুযায়ী সঠিক নয় তাহলে সঠিক অধ্যায় ও প্রশ্নটি অথবা কোন প্রকার ভুল থাকলে আমাদের কে জানান ইমেইল করে kabirdepart@gmail.com

Percentage

Correct :

Wrong :

  • 1. If x percent of 40 is y, then 10x equals?

  • x % of 40 = y 

    40x/100 = y 

    x = 100y/40 

    x = 5y/2 

    10x = 25y

  • 2. During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, What was the total number of games the team played?

  • Total number of games = x
    of games won in first 100 = .8 * 100
    number of games won in remaining games = .5 * (x-100)
    number of games won in entire season = .7x

    Now,
     .7x = .8 * 100 + .5 * (x-100)
    Or, .7x - .5x = 80 - 50
    Or, .2x = 30
    Or, x = 300/20 = 150

  • 3. In a town, 64 percent of the population is employed, and 48 percent of the population is employed males. What percentage of the employed people in that town is female?

  • We are asked to find the percentage of females in employed people.

    Total employed people 64%, out of which 48 are employed males, hence 16% are employed females. 

    (employed females)/(total employed people)

    =16/64

    =1/4

    =25%

  • 4. Out of 7500 candidates 75% were offered to study in Arts and 45% in Business. How many were offered both?

  • Total sum of percentage =  (75+45)%=120%

    Percentage offered in both = 120 - 100 = 20%

    So, number of students who were offered both=  20% of 7500= 1500

  • 5. Kamal went to a shop and bought things worth Tk  25.  Out of which 30 paisa went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
  • 6. একটি গ্রামের লোকসংখ্যা ৮% হারে বেড়ে ১৬২০ হলে পূর্বের লোকসংখ্যা কত ছিল?

  • ৮% বৃদ্ধিতে বর্তমানে লোকসংখ্যা  ১০৮ জন হলে পূর্বে ছিল ১০০ জন

    অতএব,

    বর্তমানে লোকসংখ্যা ১৬২০ জন হলে পূর্বে ছিল (১০০*১৬২০)/১০৮=১৫০০ জন

  • 7. If 40% of all women are voters and 52% of population are women, what % of the population are women voters?
  • 8. The rainfall in January and February was 2.5 inches and 4.0 inches respectively. What was the 9% increase in rainfall in February?
  • 9. An amount is first discounted by 20% and then discounted again by 12.5%. What is the single discount in %'?
  • 10. A product is sold at a discount by 8%. By how much 9% (approximately) the original price was higher than the discounted price?
  • 11. The price of tea being increased by 20%, a man reduces his consumption by 20%. By how much percent will his expenses for tea be decreased?
  • 12. 0.01 is what percent of 0.1
  • 13. What percent of 200 is 0.001 % of 22X53?
  • 14. A man buys a television set that lists for Tk. 36000 at 10% discount. He gets an additional 2% discount for paying cash. How much does he actually pay in Tk.?
  • 15. কোন শহরে লোকসংখ্যা ১০ লক্ষ। যদি পুরুষের ১০% বৃদ্ধি পায় এবং স্ত্রীলোকদের সংখ্যা ৬% কমে যায়, তবে শহরের লোকসংখ্যার কোন পরিবর্তন হয় না। ঐ শহরের পুরুষের সংখ্যা কত?
  • 16. ২ এর কত শতাংশ ২.৫ হবে?
  • 17. ৬০ জন ছাত্রের মধ্যে ৪২ জন ফেল করলে পাশের হার কত?

  • পাশ করে=(৬০-৪২)=১৮ জন

    সুতরাং পাশের হার=(১৮/৬০)×১০০=৩০%

  • 18. In a class, 120 students are male and 100 students are female. 25% of the male students and 20% of the female students are engineering students. 20% of the male engineering students and 25% of the female engineering students passed the final exam. What percentage of engineering students passed the exam?
  • 19. Mr. Bakhtiar works in the procurement department of a library. Under a new purchase policy, he increased the total number of books in the library by 20%. But soon afterwards, as part of the library cleaning process, 10% of the total library book stock is disposed of. What is the net change over the initial number of books in the library?
  • 20. If 32% of 650 is equal to 2/3rd of x, what is the value of x?
  • 21. The salaries of A, B, C are in the ratio 2:3:5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new radio of their salaries?
  • 22. If 35% of a number is 175, then what percent of 175 is that number?

  • C/A: 285.71%

  • 23. A shopkeeper sells 25 articles at Tk. 45 per article after giving 10% discount and earns 50% profit. If the discount is not given, the profit gained is
  • 24. In an election a candidates who gets 84% of the votes, is elected by a majority of 476. What is the total number of votes polled?

  • Let the total number of votes polled be x.

    Then, votes polled by other candidate = (100 - 84)% of x = 16% of x.

    ∴ 84% of x - 16% of x = 476

    => (68/100)x=476

    => x=(476∗100)/68=700.

     

  • 25. A student has to obtain 33% of the marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are

  • Given that the student got 125 marks and still he failed by 40 marks

    => The minimum pass mark = 125 + 40 = 165

    Given that minimum pass mark = 33% of the total mark

    => Total Mark×(33/100)=165

    => Total Mark=16500/33 =500

  • 26. A shopkeeper sold article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?

  • Let C.P. be Tk.100.

    Then, S.P. = Tk.123.50

    Let marked price be Tk. x. Then, 95/100 x = 123.50

    x = 12350/95 = Tk.130

    Now, S.P. = Tk.130, C.P. = Tk.100

    Profit % = 30%.

  • 27. একটি ঘরের দৈর্ঘ্য ২০% বৃদ্ধি পেল এবং প্রস্থ ১০% হ্রাস পেল, ক্ষেত্রফল শতকরা কতটুকু বৃদ্ধি পেল? 

  • ২০% বৃদ্ধি তে ,
    দৈর্ঘ্য ১০০ হলে পরবর্তী দৈর্ঘ্য = ১২০
    ১০% হ্রাসে ,
    প্রস্থ ১০০ হলে প্রস্থ = ৯০
     ক্ষেত্র ফল = (১২০ x  ৯০) = ১০৮০০
    প্রথম ক্ষেত্রে ক্ষেত্রফল = (১০০ x ১০০)= ১০০০০
    বৃদ্ধি = (১০৮০০-১০০০০) =৮০০
    তাহলে , শতকরা বৃদ্ধি   = (৮০০/১০০০০) X ১০০ = ৮%

     

  • 28. কোন পণ্যের পূর্বমূল্য : বর্তমান মূল্য =৫:৭ হলে, শতকরা মূল্য বৃদ্ধি কত? 

  • মূল্যের অনুপাতের পারথক্য=৭-৫=২
    সুতরাং,শতকরা মূল্য বৃদ্ধি=(২/৫)X১০০=৪০%

  • 29. If the price of an item is increased by 10% then decreased by then 10% percent the net effect on the price of the item is?

  • Let, the price=100

    10% increased=(100×110)/100=110

    10% decreased= (110×90)/100=99

    So, decreased by (100-99)=1%

  • 30. In a Bank.30% of the applicants are from Rajshahi district and 20% of them from Rajshahi city. What percent of the total applicants are from Rajshahi City?

  • Let, Total applicants=100

    Applicants of Rajshahi district=100×30%=30

    Applicants of Rajshahi city=30×20%=6

    So, Total applicants are from Rajshahi City=6%

  • 31. If the sides of a square increase by 10%,how much will the area be increased in percentage?

  • Original side length: x
    New side length: x + 10% x = 1.1 x

    Original area = x^2
    New area = (1.1 x)^2 = 1.21 x^2

    So we've increased area by factor of 1.21 = 1 + 0.21 = 1 + 21%

    So we've increased area by 21%

  • 32. When a commodity is sold for Tk. 49, there is a loss 2%. What is the cost price of the commodity?

  • Cost price=(49×100)/98 = Tk. 50

  • 33. What is 10% of Y/3 , If 2Y/3 is 10% of 400?

  • 2Y/3=10% of 400

    => 2y/3=40

    => y=60

     

    So, Y/3 × 10%

      = 60/3 × 10%

      =20× 10%

      = 2(Ans.)

  • 34. Two third of the faculty members of a department are female. Twelve of the male faculty members are unmarried, while 60% of them are married. What is the total number of faculty members in the department?

  • 40% (married) of total male = 12

    100% of total male = 12*100/40

                                        = 30

    If total number of faculty = x

    then, total number of male faculty = x - 2x/3 = (3x-2x)/3 = x/3

    Thus,

    x/3 = 30

    x = 30*3 = 90

  • 35. In one year, the population of a city increased by 20%. The next year, it decreased by 10%. What was the percentage increase in the population over the two years?

  • if In year 1 population is 100

    in year 2, population is 120

    Now, in year 3,

    10% decrease means,

    if population was 100, it decreased by to 90

    if population was 1, it decreased by to 90/100

    if population was 120, it decreased by to 90*120/100 = 108

     

    Thus, increase in population from year 1 = 108 - 100 = 8

  • 36. A fuel tank is 50% full. If 8 gallons of fuel is removed, then the tank remains 10% full. What is the capacity of the tank in gallons?

  • (50 - 10)% = 40% means 8 gallons of fuel

    1% means 8/40 gallons of fuel

    100% means 8*100/40 gallons of fuel

                       = 20 gallons of fuel

  • 37. In a class, 50% of the male students and 2/3 of the female students speak French. If there are ¾ as many girls as boys, what fraction of the entire class speaks French?

  • x=# of boys in the class
    y=# of students that speak French

    Therefore we are looking for y / (total number in class). But the total number in the class is boys plus girls,
    so x + 3/4x=7/4x The 3/4 is because they told us there are 3/4 as many girls as boys. So now

    y / (total number in class) = y / (7/4x)

    Now we know that the number of students that speak French are:
    1/2 boys +2/3 girls or 1/2x + 2/3(3/4x) = y = 1/2x + 6/12x = x Therefore y / (7/4x) = x / (7/4)x = 4/7

    So the curve ball here is that the number that speak French just happens to be equal to the number of boys in the class, and boys make up 4/7 of the class as well.

  • 38. What percentage of numbers from 11 to 90 has 0 or 5 in the unit’s digit?

  • 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90 => 16 Numbers

    And amount of numbers from11 to 90 = (90 - 11) +1 = 79 + 1 = 80

    Percentage of numbers = 16*100/80 = 20%

  • 39. In a class, 120 students are finance major and 100 students are marketing major. 25% of the finance students and 20% of the male finance students and 25% of the male marketing students passed the final exam. What percentage of male students passed the exam?
  • 40. A shopkeeper combined X liters of a solution containing 10% of certain material Q, with 10 liters of another solution that contained 2% of that material Q, to produce Z liters of a solution that had 5% of Q. What is the value of X?
  • 41. একটি বই ৫% কমিশনে বিক্রয় করা হয়। বইটির প্রকৃত বিক্রয়মূল্য ৭২০ টাকা হলে বইটি কত টাকায় ক্রয় করা যাবে? 

  • ১০৫% এর আসল মূল্য ৭২০ টাকা

    ১০০% এর আসল মুল্য ৭২০*১০০/১০৫ টাকা = ৬৮৫.৭১ টাকা

  • 42. A survey of n people in the town Afound that 50% of them prefer Brand X. Another survey of 100 people in the town B found that 60% prefer Brand X. In total, 55% of allthe people surveyed together prefer Brand x what is the total number of people surveyed?

  • Sol: 50% (n) + 60% (100 ) = 55% (n + 100)
    Solving we get n = 100

    n + 100 = 100 + 100 = 200

  • 43. In a class, 120 students are male and 100 students are female 25% of the male students and 20% of the female students are engineering students. 20% of the male engineering students and 25% of the female engineering students passed the final exam, what percentage of engineering students passed the exam?

  • male engineering student = 25*120/100 = 30

    female engineering student = 20*100/100 = 20

    total engineering student = 30 + 20 = 50

    now,

    male engineering students that passed = 20*30/100 = 6

    female engineering students that passed = 25*20/100 = 5

    total students that passed = 6 + 5 = 11

    now,

    percentage of engineering students that passed the exam = 11*100/50 = 22%

  • 44. A company generated revenue of Tk. 125,000 in 2012which was 12.5% of its gross revenue. In 2013, the gross revenue increased by Tk. 250,000, what is the percentage increase in the revenue in 2013?
  • 45. If w is 10 percent less than x, and y is 30 percent less than z, then wy is what percent less than xz?
  • 46. What percentage of numbers from 1 to 80 has 0 or 5 in the unit's digit?
  • 47.  in a group of students,80% of the students weigh less than 60 kg and a total of 32 students weigh less than 50 kg .If 60% of the students weigh less than 50 kg. If 60% of the students weigh at least 50 kg.How  many of the students weigh at least 50 kg but less than 60 kg?  
  • 48. What is 2x%of 50?
  • 49. The number of passengers on dhaka-rangpur route inceeased by 30% when the fare was reduced by 10%.what will be the percentage change in revenue?

  • suppose,
    before passenger was =100
    before fare was=100 tk
    so, earning was= (100 x100)=10000 taka
    at 30% increase,
    total passenger =100+30=130
    at 10% decrease,
    fare=90 taka

  • 50. A seller gave 5% discount on the tag price of a book and made a profit of 25% on cost.if the cost of the book was tk380,what was the tag price?


  •  

  • 51. A seller gave 5% discount on the tag price of a book and made a profit of 25% on cost.if the cost of the book was tk380,what was the tag price?


  •  

  • 52. কোন স্কুলে ৭০% শিক্ষার্থী ইংরেজি এবং ৮০% শিক্ষার্থী বাংলায় পাস করেছে। কিন্তু ১০% উভয় বিষয়ে ফেল করেছে ।যদি উভয় বিষয়ে ৩০০ জন শিক্ষার্থী পাস করে থাকে,তবে ঐ স্কুলে কতোজন শিক্ষার্থী পরীক্ষা দিয়েছে?

  • শুধু ইংরেজিতে ফেল করেছে (১০০-৭০-১০)% =২০%

       ’’  বাংলায়    ’’   ’’   (১০০-৮০-১০)%=১০%

     সুতরাং, উভয় বিষয়ে ফেল করে (২০+১০+১০)=৪০%

     সুতরাং,   ’’   ” পাশ করেছে(১০০-৪০)=৬০%

      উভয় বিষয়ে ৬০ জন পাশ করে যখন শিক্ষার্থী =১০০

      ’’    ”  ৩০০  ”  ”  ”   ”    ”         
      =১০০*৩০০/৬০=৫০০ জন 

  • 53. একটি সংখ্যার ২০ শতাংশের ৮০ শতাংশ যদি ১২.৮ হয়, সংখ্যাটি কত?  

  •  

    মনে করি সংখ্যাটি x; শর্তমতে, x X ২০%X৮০%=১২.৮

      =x X 20/100X80/100=12.8 = x/৫ X ৪/৫= ১২.৮=৪X/২৫=১২.৮

    =৪x=৩২০ =x =৩২০/৪=৮০ 

  • 54. A man buys Tk. 50 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?
  • 55. 8% of the people eligible on vote are between 18 and 21. In an election 85% of those (between 18 and 21) actually voted.n What is the percentage of those voters (between 18 and 21) in terms of total eligible voters?  
  • 56. A hospital has enough pills on hand to treat 10 patients for 14 days. How long will the pills last if there are 35 patients?

  • 10 patients last for 14 days
    1 patients last for 10 x 14 days
    35 patients last for 10 x 14/35=4 days
     

  • 57. On a test consisting of 80 questions, Nasir answered 75% of the first 60 questions correctly. What percent of the other 20 questions does the need to answer correctly for his grade on the entire examination to be 80%?  
  • Here,
    80% of 80 question= 80 X 80/100 =64
    so ,he needs to answer total 64 question correctly
    now, as he answered 75% of 60 question correctly=75/100 x 60 =45
    so, remaining question=64-45=19 to answer total 64 question
    and 19 of 20 =19/20 x 100=95%
  • 58. The population of a country doubled every 10 years from 1960 to 1990. What was the percent increase in population during this time?
  • 1990-1960=30 years
    if in the first 10 years ,the population was x,then after 30 years
    it would be =x+2x+3x=7x
    so, increase=7x/x  X 100%=700%
  • 59. If the price of an item is increased by 10% and then decreased by 10%, the net effect on the price of the item is-

  • suppose,
    price of product=100 tk
    at 10% increase,
    price=110 tk
    again,
    at 10% decrease,
    price=110-11 tk=99 tk
    so, price reduced=100-99 tk=1 tk
    so, reduced 1%

     

  • 60. A book sells for Tk. 65. This price gives the seller a profit of 30% on his cost. What would be the new selling price if he cuts his profit to 10% of the cost?

  • at 30% profit,
    selling price 130 tk when cost 100 tk
    selling price  1 tk when cost 100/130 tk
    selling price 65 tk then cost 100 X 65/130 tk=50 tk
    then, at 10% profit,
    when buying price 50 tk then selling price=50 X 110/100= 55 tk
     

  • 61. A restaurant meal costs taka 35.50 and there was no tax. If the tip was more than 10% and less than 15% of the cost of the meal then the total amount paid must have been between----
  • 62. 20% of 0.2 is-
  • 63. 40% of 200 is what percent of 160?
  • 64. An item is sold for taka 65, giving the retailer a profit of 30% of the cost. What will be the new retail price if the retailer cuts his profit to 10% of costs?

  • at 30% profit,
    selling price 130 tk when cost 100 tk
    selling price  1 tk when cost 100/130 tk

  • 65. If 25% of 220 equals 5.5% of w, then w is ----

  • 25% of 220 =220 X .25 =55
    55 is 5.5% of = 55/5.5 X 100 = 1000

  • 66. A retailer buys a Panjabi and a Fatua jointly at Tk. 500. If he sells the Fatua at 10% profit and the Panjabi at 5% loss, then he gets Tk. 520 as total sales price. What is the cost price of the Fatua?
  • 67. In a village the growth rate of population is 5% every year. There are 1600 people in the beginning of 2008 what will be the approximate number of people in the beginning of 2011?
  • 68. Zahir, after joining to a new job, received a 10% Raise each year for 4 consecutive years. If his salary after the 4th raise is Tk. 4392.30, what was his starting salary?
  • 69. Raad answered 75% of the questions on a test correctly. If he answered 18 questions out of the first 22 correctly, and two-third of the remaining questions correctly, how many questions were on the test?
  • 70. Rabeya’s father contributes to her savings by giving her 25% of her total savings. If Rabeya saves Tk. 150 in May, Tk. 200 in June and Tk. 300 in July, how much will she have savings at the end of July?
  • 71. Which of the following fractions is the equivalent of 0.5%?
  • 72. In a certain exam, 65% students passed in Math and 50% passed in English. If 25% of the students have passed in both the subjects, what percent of the students have failed in both Math and English?

  • only passed in math=(65-25)%=40%
    only passed in english=(50-25)%=25%
    total passed=(40+25+25)%=90%
    so,failed=100-90=10%

  • 73. A school has a total enrolment of 90 students. There are 30 students taking Physics, 25 taking English, and 13 taking both. What percentage of the students is taking either Physics or English?
  • 74. What percent of 2/5 is 1/25?
  • 75. A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?          

  • Let S be the selling price of 1 article.
    Therefore, the selling price of 100 articles = 100 S. --(1)
    The profit earned by selling these 100 articles = selling price of 75 articles = 75 S -- (2)
    We know that Selling Price (S.P.) = Cost Price (C.P) + Profit -- (3)
    Selling price of 100 articles = 100 S and Profit = 75 S from (1) and (2). Substituting this in eqn (3), we get
    100 S = C.P + 75 S. Hence, C.P = 100 S - 75 S = 25 S.
    Profit % = 300%

  • 76. If the price of an item is increased by 10% and then decreased 10% , the net effect on the price of the item is---

  • at 10% increase,
    if  previous price 100 then current price (100+10)=110 tk
    at 10% decrease,
    if  previous price 100 then current price (110-11)=99 tk
    so, net effect on the price of the item is a decrease of 1%

  • 77. Successive discounts of 20% and 12% are equivalent to a single discount of:

  • suppose Cost Price is tk 100
    then 20% discount means Selling Price is tk .80
    but again on this price there's a dicount of 12%
    therefore, the final  discount =80 X 12/100=9.6 %
    therefore, total discount = 20+9.6=29.6%

  • 78. In a class of 200 students, 40 percent are girls. 25 percent of the boys and 10 percent of the girls signed up for a tour to Cox’s bazar. What percent of the class signed up for the tour?

  • as 40% are girls then there are = 200 X 40/10 = 80 girls
    so, number of boys =200-80=120 boys
     25 percent of the boys = 120 X 25/100 = 30 boys
    10 percent of the girl =80X 10/100 =8 girls
    so, total student =(30+8)=38 
    percent of the class signed up for the tour=38/200 X 100 =19%

  • 79. A restaurant meal costs Tk. 35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the metal, then the total amount paid must have been between---
  • 80. The price of a certain DVD Player is discounted by 10 percent, and the reduced price is then discounted again by 10 percent. The series of successive discounts is equivalent to a single discount of---
  • 81. Since 1999, Roby has gained 2 kilograms of weight every year. In 2009 he was 25% heavier than in 1999. How much did Roby weigh in 2005?
  • 82. A solution that contains 20% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight in the new solution is—
  • 83. The price of a shirt is increased by 20%. How many shirts can be purchased for the amount of money that was used to buy 300 shirts before?
  • 84. The household expenses of a family went up by 20%. By how many percent must the family reduce household expenditure so that expenses remain same as before?
  • 85. In a class 40% of the students enrolled for Math and 70% enrolled for Economic. If 15% of the students enrolled for both Math and Economics, What % of the students of the class did not enroll for either of the two subjects?
  • 86. What is the maximum percentage discount that a merchant can offer on her Marked Price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?
  • 87. A school has raised 75% of the amount it needs for a new building by receiving an average donation of Tk 60 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, how much must the remaining people donate per person?

  • suppose,
    total people 100
    60% means,
    60  people gve 60 tk,
    then total= 60x60=3600 tk
    people remain= 40 
    money remin=3600x100/75=4800-3600=1200 tk
    so  remaining per people donate =1200/40=30 tk

  • 88. Buffet dinner at a restaurant costs Tk. 3550(excluding sales tax). If the sales tax was more than 10 percent but less than 15 percent of the pre-tax cost of the dinner, then the total amount paid must have been between---

  • The minimum value of 10% including tax =- 35.50+3.55 = 39.05

    And the maximum value of 15% including tax = 35.50+ 5.325 = 40.825

    So, the total amount will be paid Tk. 39 and tk. 41

  • 89. Two outlets of a motor manufacturing company reported that revenue from outlet x in 2013 was down 11 percent from 2012 and revenue from outlet Y in 2013 were up 7 percent from 2012. If total revenue from outlet X & Y in 2013 was up 1 percent from 2012, what is the ratio of revenue from outlet X in 2012 revenue from outlet Y in 2012?
  • 90. Mr. Ahsan is insured completely for Tk. 50000 of damages to his car. For any damage above Tk. 50000 the insurance company will pay Tk. 50000 plus 20% of the rest of the damage amount. For a recent accident, Mr. Ahsan was paid 56000 by the insurance company. What was the total amount of the damage estimated?

  • damage insured=50000 tk
    damage paid by company=56000 tk
    damage extra paid=6000 tk

  • 91. A survey showed that 63% of Bengali people like chicken where as 76% like fish. If x% on them like both fish and chicken, then what is the range of x?

  • suppose,
    people like both x%
    total people 100%
    here,
    x%=(63+76)%-100%=39%

  • 92. In a college, 45% of the students are boys. If 40% of the boys and 20% of the girls went on a picnic, what percentage of the total students went to the picnic?

  • boys =45%
    so,girls=100-45=55%

    boys went to picnic=40%  of 45 %=18%
    girls went to picnic=55% of 20%=11%
    total student=(18+11)=29%

  • 93. The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount.The rate percent is:

  • Let T.D. be Tk. 1.

    Then, B.D. = Tk. 11/10 = Tk. 1.10.

    Sum = Tk. (1.10 x 1)/(1.10 – 1)

    = Tk. (110/10) = Tk. 11.

    S.I. on Tk. 11 for 2 years is Tk. 1.10

    So, Rate = {(100 x 1.10)/( 11 x 2)}%

    = 5%.

  • 94. The true discount on a bill of Tk. 540 is Tk. 90. The banker's discount is:

  • P.W. = Tk. (540 - 90) = Tk. 450.

    So, S.I. on Tk. 450 = Tk. 90.

    S.I. on Tk. 540 = Tk. {(90/450)x 540} = Tk. 108.

    So, B.D. = Tk. 108.

  • 95. The present worth of a sum due sometime hence is Tk. 576 and the banker's gain is Tk. 16. The true discount is:

  • T.D. = √(P.W. x B.G.) = √(576 x 16) = 96.

  • 96. The banker's gain on a certain sum due 1(1/2) years hence is 3/25 of the banker's discount.  The rate percent is:

  • 97. The banker's gain on a bill due 1 year hence at 12% per annum is Tk. 6. The true discount is:

  • T.D. = (B.G. x 100)/( R x T)

    = Tk. (6 x 100)/(12 x 1)  = Tk. 50.

  • 98. The present worth of a certain bill due sometime hence is Tk. 800 and the true discount is Tk. 36. The banker's discount is:

  • B.G. = (T.D.)2 / P.W.

    = Tk. (36 x 36)/800= Tk. 1.62

    B.D. = (T.D. + B.G.) = Tk. (36 + 1.62) = Tk. 37.62

  • 99. The certain worth of a certain sum due sometime hence is Tk. 1600 and the true discount is Tk. 160. The banker's gain is:

  • B.G. = (T.D.)2/ P.W.

    = Tk. (160 x 160)/1600= Tk. 16.

  • 100. The banker's discount of a certain sum of money is Tk. 72 and the true discount on the same sum for the same time is Tk. 60. The sum due is:

  • Sum = (B.D. x T.D.)/( B.D. - T.D.) = Tk. (72 x 60)/( 72 – 60)

    = Tk. (72 x 60)/ 12 = Tk. 360.

  • 101. The banker's gain on a sum due 3 years hence at 12% per annum is Tk. 270. The banker's discount is:

  • T.D. = (B.G. x 100)/( R x T)

    = Tk. (270 x 100)/( 12 x 3)

    = Tk. 750.

    So, B.D. = Tk.(750 + 270) = Tk. 1020.

  • 102. The banker's discount on a sum of money for 1(1/2) years is Tk. 558 and the true discount on the same sum for 2 years is Tk. 600. The rate percent is:

  • B.D. for 3/2 years = Tk. 558.

    B.D. for 2 years = Tk. {558 x (2/3) x 2}

    = Tk. 744

    T.D. for 2 years = Tk. 600.

    So, Sum = (B.D. x T.D.)/( B.D. - T.D)

    = Tk. (744 x 600)/144 = Tk. 3100.

    Thus, Tk. 744 is S.I. on Tk. 3100 for 2 years .

    So, Rate = (100 x 744)/(3100 x 2)% = 12%

  • 103. The banker's gain of a certain sum due 2 years hence at 10% per annum is Tk. 24. The present worth is:

  • T.D. = (B.G. x 100)/( Rate x Time)

    = Tk. (24 x 100)/( 10 x 2)

    = Tk. 120.

    So, P.W. = (100 x T.D.)/( Rate x Time)

    = Tk. (100 x 120)/( 10 x 2) = Tk. 600.

  • 104. The banker's discount on Tk. 1600 at 15% per annum is the same as true discount on Tk. 1680 for the same time and at the same rate. The time is:

  • S.I. on Tk. 1600 = T.D. on Tk. 1680.

    So, Tk. 1600 is the P.W. of Tk. 1680,

    i.e., Tk. 80 is on Tk. 1600 at 15%.

    So, Time = (100 x 80)/( 1600 x 15) year

    = 1/3 year

    = 4 months.

  • 105. The banker's discount on a bill due 4 months hence at 15% is Tk. 420. The true discount is:

  • T.D. = (B.D. x 100)/{100 + (R x T)}              

    = Tk. (420 x 100)/{100 + (15 x 1/3)}

    = Tk. (420 x 100)/105

    = Tk. 400.

  • 106. Sakshi invests a part of Tk. 12,000 in 12% stock at Tk. 120 and the remainder in 15% stock at Tk. 125. If his total dividend per annum is Tk. 1360, how much does he invest in 12% stock at Tk. 120?

  • Let investment in 12% stock be Tk. x.

    Then, investment in 15% stock = Tk. (12000 - x).

    So, {(12/120) x x} + {(15/125) x (12000 - x)} = 1360.

    => x/10 + (3/25) x (12000 - x) = 1360.

    => 5x + 72000 - 6x = 1360 x 50

    => x = 4000.

  • 107. The cost price of a Tk. 100 stock at 4 discount, when brokerage is (¼)% is:

  • C.P. = Tk. (100 - 4 + (¼)) = Tk. 96.25

  • 108. The market value of a 10.5% stock, in which an income of Tk. 756 is derived by investing Tk. 9000, brokerage being (1/4)%, is:

  • For an income of Tk. 756, investment = Tk. 9000.

    For an income of Tk. 21/2, investment = Tk. (9000/756) x (21/2)

    = Tk. 125.

    So, For a Tk. 100 stock, investment = Tk. 125.

    Market value of Tk. 100 stock = Tk. (125 – ¼)

    = Tk. 124.75

  • 109. A 12% stock yielding 10% is quoted at:

  • To earn Tk. 10, money invested = Tk. 100.

    To earn Tk. 12, money invested = Tk. (100/10) x 1

    = Tk. 120.

    So, Market value of Tk. 100 stock = Tk. 120.

  • 110. A man invested Tk. 1552 in a stock at 97 to obtain an income of Tk. 128. The dividend from the stock is:

  • By investing Tk. 1552, income = Tk. 128.

    By investing Tk. 97, income = Tk. (128/1552) x 97

    = Tk. 8.

    So, Dividend = 8%

  • 111. By investing Tk. 1620 in 8% stock, Michael earns Tk. 135. The stock is then quoted at:

  • To earn Tk. 135, investment = Tk. 1620.

    To earn Tk. 8, investment = Tk. (1620/135) x 8 = Tk. 96.

    So, Market value of Tk. 100 stock = Tk. 96.

  • 112. A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:

  • For an income of Re. 1 in 9% stock at 96, investment = Tk. (96/9)

    = Tk. 32/3

    For an income Re. 1 in 12% stock at 120, investment = Tk. 120/12

    = Tk. 10.

    Ratio of investments = 32/3 : 10

    = 32 : 30 = 16 : 15.

  • 113. Tk. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:

  • Let the investment in 9% stock be Tk. x.

    Then, investment in 10% stock = Tk. (9800 - x).

    (9/75) x x = (10/80) x (9800 - x)

    => 3x/25 = (9800 – x)/8

    => 24x = 9800 x 25 - 25x

    => 49x = 9800 x 25

    => x = 5000.

  • 114. A man invested Tk. 4455 in Tk. 10 shares quoted at Tk. 8.25. If the rate of dividend be 12%, his annual income is:

  • Number of shares = (4455/8.25) = 540.

    Face value = Tk. (540 x 10) = Tk. 5400.

    Annual income = Tk. (12/100) x 5400

    = Tk. 648.

  • 115. A 6% stock yields 8%. The market value of the stock is:

  • For an income of Tk. 8, investment = Tk. 100.

    For an income of Tk. 6, investment = Tk. (100/8) x 6 =  Tk. 75.

    So, Market value of Tk. 100 stock = Tk. 75.

  • 116. By investing in 16(2/3)% stock at 64, one earns Tk. 1500. The investment made is:

  • To earn Tk. 50/3, investment = Tk. 64.

    To earn Tk. 1500, investment = Tk. (64 x (3/50) x 1500)

    = Tk. 5760.

  • 117. A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:

  • Dividend on Tk. 20 = Tk. (9/100) x 20

    = Tk. 9/5.

    Tk. 12 is an income on Tk. 100.

    So, Tk. 9/5 is an income on Tk.(100/12) x (9/5)

    = Tk. 15.

  • 118. Which is better investment: 11% stock at 143 or 9(3/4)% stock at 117?

  • Let investment in each case be Tk. (143 x 117).

    Income in 1st case = Tk. ((11/143) x 143 x 117) = Tk. 1287.

    Income in 2nd case = Tk. {39/(4 x 117)x 143 x 117} = Tk. 1394.25

    Clearly, 9(3/4)% stock at 117 is better.

  • 119. A man bought 20 shares of Tk. 50 at 5 discounts, the rate of dividend being 13(1/2). The rate of interest obtained is:

  • Investment = Tk. [20 x (50 - 5)] = Tk. 900.

    Face value = Tk. (50 x 20) = Tk. 1000.

    Dividend = Tk. (27/2 x 1000/100)

    = Tk. 135.

    Interest obtained = ((135/900) x 100)%

    = 15%

  • 120. In order to obtain an income of Tk. 650 from 10% stock at Tk. 96, one must make an investment of:

  • To obtain Tk. 10, investment = Tk. 96.

    To obtain Tk. 650, investment = Tk. (96/10) x 650

    = Tk. 6240.

  • 121. A trader dealing in pressure cookers reduced the price by 20% as a result of wich his sale went up by 80%. What is the net effect of his sales income?
  • 122. An employee pays 3 workers – X,Y and Z, a total of Tk. 610 in a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?
  • 123. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

  • Increase in 10 years = (262500-175000) = 87500

    Increase % = (87500/175000 × 100)% = 50%

    So, Required average = (50/10)% = 5%

  • 124. Rajeev buys good worth Tk. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

  • Rebate = 6% of Tk. 6650 =Tk. (6/100 × 6650) = Tk. 399.

    Sales tax = 10% of Tk. (6650-399) =Tk. (10/100 × 6251) = Tk. 625.10

    So, Final amount = Tk. (6251+625.10) = Tk. 6876.10

  • 125. Jami went to the stationers and bought things worth Tk. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

  • Let the amount taxable purchases be Tk. X

    Then, 6% of x = 30/100

    => x=(30/100 × 100/6) = 5

    So, Cost of tax free items = Tk. [25-(5+0.30)] = Tk. 19.70

  • 126. Two tailors X and Y are paid a total of Tk. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?

  • Let the sum paid to Y per week be Tk. Z

    Then, z+120% of z = 500

    =>  z+ 120z/100 = 550

    => 11z/5 = 550

    => 11z/5 = 550

    => z = (550×5)/11 = 250

  • 127. Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

  • Total number of votes polled = (1136+7636+11628) = 20400.

    So, Required percentage = (11628/20400 × 100)% = 57%

  • 128. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

  • Number of valid votes = 80% of 7500 = 6000.

    So, Valid votes polled by other candidate = 45% of 6000

    = (45/100 × 6000) = 2700

  • 129. A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

  • Let the number be x.

    Then, error = 5x/3 – 3x/5 = 16x/15

    Error% = (16x/15 × 3/5x × 100)% = 64%

  • 130. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

  • 5% of A + 4% of B =2/3(6% of A + 8% of B)

    => 5A/100 + 4B/100 = 2/3 (6A/100 + 8B/100)

    => 1A/20 + 1B/25 = 1A/25 + 4B/75

    => (1/20 – 1/25)A = (4/75 – 1/25)B

    => 1A/100 = 1B/75

    A/B = 100/75=4/3

    So, Required ratio = 4:3

  • 131. In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?

  • Let the number of students be x. Then,

    Number of students above 8 years of age = (100-20)% of x = 80% 0f x.

    So, 80% of x = 48 + 2/3 of 48

    => 80x/100 = 80

    => x = 100

  • 132. If 20% of a = b, then b% of 20 is the same as:

  • 20% of a = b

    =>20/100 ×a =b

    So, b% 20 = (b/100×20) = (20a/100 × 1/100 × 20)

    =4a/100 = 4% of a

  • 133. If A = x% of y and B = y% of x, then which of the following is true?

  • X% of y = (x/100 × y) = (y/100 × x) = y% of x

    So, A= B

  • 134. What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?

  • Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

    Number of such number =14

    So, Required percentage = (14/70 × 100)% = 20%

  • 135. A fruit seller had some apples. He sells 40% apple and still has 420 apples. Originally, he had:

  • Suppose originally he had x apples.

    Then, (100-40)% of x =420.

    => 60/100 × x = 420

    => x = (420×100)/60 = 700.

  • 136. Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

  • Let their marks be (x+9) and x.

    Then, x+9 = 56/100 (x+9+x)

    =>  25 (x+9) = 14(2x+9)

    => 3x = 99

    => x=33

    So, Their marks are 42 and 33.

  • 137. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

  • Number of runs made by running = 110 –(3×4+8×6)

    = 110 –(60)

    = 50

    So, Required percentage = (50/110 × 100)% =45 5/11%

  • 138. Anis, who owns (200/3)% of a factory, sell half of his share  of Tk. 33,333. The value of the entire factory is-

  • (200/3)% = 200/(3X100) = 2/3

    half of 2/3 = 1/2 * 2/3 = 1/3

    1/3 costs 33333

    entire factory costs 99999

  • 139. In a survey, 30% of the people surveyed owned a personal computer and 75% owned a cellular telephone. If 25% owned both a cellular telephone and a personal computer, then the percentage of the people who does not have either of the instrument?

  • Only Cellular telephone (75-25)% = 50%

    only pc (30-25)% = 5%

    So, either cellular or pc and both = (50+5+25)% = 80% 

    the percentage of the people who does not have either of the instrument = (100-80)% = 20%

  • 140. If the true discount on s sum due 2 years hence at 14% per annum be Tk. 168, the sum due is:      

  • PRESENT WORTH= (100×TRUE DISCOUNT.)/(R×T)= (100×168)/(14×2)=600

    Sum= (PRESENT WORTH + TRUE DISCOUNT.) = Tk. (600+168) = Tk. 768

  • 141. The present worth of Tk. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:      

  • Required sum = PRESENT WORTH of Tk. 702 due 6 months + PRESENT WORTH of Tk. 702 due 1 year hence

    = Tk. [(100×702)/100+8(1/2)]+[(100×702)/100+(8×1)]

    = Tk. (675+650)

    = Tk. 1325

  • 142. The simple interest and the true discount on a certain sum for a given time and at a given rate are Tk. 85 and Tk. 80 respectively. The sum is:    

  • Sum= S.I × TRUE DISCOUNT./(S.I)-(TRUE DISCOUNT.)

    =85×80/(85-80)

    =Tk. 1360

  • 143.  The interest on Tk. 750 for 2 years is the same as the true discount on Tk. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:      

  • S.I. on Tk. 750 = TRUE DISCOUNT. on Tk. 960.

    This means PRESENT WORTH of Tk. 960 due 2 years hence is Tk. 750.

    Or, TRUE DISCOUNT= Tk. (960-750)=Tk. 210

    Thus, S.I on Tk. 750 for 2 years is Tk. 210.

    Rate = (100×210)/(750×2)% = 14%

  • 144. Tk. 20 is the true discount on Tk. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?      

  • S.I. on Tk. (260-20) for a given time = Tk. 20

    S.I. on Tk. 240 for half the time = Tk. 10.

    TRUE DISCOUNT on Tk. 250 = Tk. 10

    So, TRUE DISCOUNT. on Tk. 260 = Tk. (10/250)×260= Tk. 10.40

  • 145. The present worth of Tk. 2310 due 2×(1/2) years hence, the rate of interest being 15% per annum, is:      

  • PRESENT WORTH = Tk. [(100×2310)/100+(15×5/2)] = Tk. 1680

  • 146. The true discount on Tk. 1760 due after a certain time at 12% per annum is Tk. 160. The time after which it is due is:      

  • PRESENT WORTH = Tk. (1760-160) = Tk. 1600.

    S.I. on Tk. 1600 at 12% is Tk. 160

    So, Time = (100×160)/(1600×12)= 5/6 years = (5/6)×12 months = 10 months

  • 147. A man buys a watch for Tk. 1950 in cash and sells it for Tk. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:      

  • S.P. = PRESENT WORTH of Tk. 2200 due 1 year hence

    = Tk. [(2200×100)/100+(10×1)]

    = Tk. 2000

    So Gain = Tk. (2000-1950) = Tk. 50.

  • 148. The true discount on a bill due 9 months hence at 16% per annum is Tk. 189. The amount of the bill is:      

  • Let P.W be Tk. X.

    Then, S.I on Tk. X at 16% for 9 months = Tk. 189.

    So, x ×16× 9/12×1/100 = 189 or x = 1575

    So, PRESENT WORTH = Tk. 1575

    So, Sum due = PRESENT WORTH + TRUE DISCOUNT = Tk. (1575+189) = Tk. 1764

  • 149. Goods were bought for Tk. 600 and sold the same for Tk. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:      

  • S.P = 102% of Tk. 600 = [(102/100)×600] = Tk. 612.

    Now, PRESENT WORTH = Tk. 612 and sum = Tk. 688.50.

    So, T.D = Tk. (688.50-612) = Tk. 76.50.

    Thus, S,I on Tk. 612 for 9 months is Tk. 76.50.

    So, Rate = [(100×76.50)/612×(3/4)]%= 16(2/3)%

  • 150. If Tk. 10 be allowed as true discount on a bill of Tk. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:      

  • S.I. on Tk. (110-10) for a certain time = Tk. 10.

    S.I on Tk. 100 for double the time = Tk. 20.

    T.D. on Tk. 120 = Tk. (120-100) = Tk. 20.

    T.D. on Tk. 110 = Tk. (20/120)×110= Tk. 18.33

  • 151. A man wants to sell his scooter. There are two offers, one at Tk. 12,000 cash and the other a credit of Tk. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?      

  • PRESENT WORTH of Tk. 12,880 due 8 months hence = Tk. [(12880×100)/100+{18×(8/12)}]

    = Tk. (12880×100)/112

    = Tk. 11500

  • 152. A trader owes a merchant Tk. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?      

  • Required money = PRESENT WORTH of Tk. 10028 due 9 months hence

    = Tk. [(10028×100)/100+{12×(9/12)}]

    = Tk. 9200

  • 153. The true discount on Tk. 2562 due 4 months hence is Tk. 122. The rate percent is:      

  • P.W. = Tk. (2562-122) = Tk. 2440 {here, P.W.=Present Worth}

    So, S.I. on Tk. 2440 for 4 months is Tk. 122

    So, Rate = [(100×122)/{2440×(1/3)}]%

    = 15%

  • 154. A man purchased a cow for Tk. 3000 and sold it the same day for Tk. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:      

  • C.P. = Tk. 3000.

    S.P. = Tk. [(3600 × 100)/{100+(10 × 2)}]

    = Tk. 3000

    Gain = 0%

  • 155. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. What is the ratio of A and B?

  • The sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B

    => 5A/100 + 4B/100 =2/3 (6A/100 + 8B/100)

    =>(5A + 4B )/100 = 2/3 (6A+8B)/100

    =>(5A + 4B ) = 4A + 16/3B

    => A = 4B/3

    => A: B = 4/3

  • 156. In a college, 45% of the students are boys. If 40% of the boys and 20% of the girls went on a picnic, what percentage on the total students went to the picnic?

  • 45% of the students are boys

    So, 55% of the students are girls

    40% of the boys and 20% of the girls

    = 40% of 45% of the students + 20% of  55% of the students

    = 18% + 11% =29% of the students

  • 157. Hasan sold an article for 56 taka which cost him x taka. If he had gained x% on his outlay, what was his cost?

  • Hasan sold an article for 56 taka which cost him x taka

    So, Profit = (56-x)

    Again he had gained x% on his outlay,

    So Profit = x*x/100

    We get,

    x2/100 = 56 - x

    x2/100 +x- 56 =

    x2 +100x -5600 = 0

    x2 + 140x -40x -5600 = 0

    x(x + 140) - 40 (x + 140) =0

    (x-40) (x+140)=0

    x=40

     

     

  • 158. If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent  increase in the area of the plot?

  • Length = x

    Width = y

    A = xy

    After increase, Length = 1.2x

    Width = 1.2y

    Area = 1.44xy

    So Increase =44%

  • 159. In a class composed of x girls and y boys what part of the class is composed of girls?

  • boys & girls = x+y

    Girl Ratio = x/(x+y)

  • 160. 75% of 0.08=?

  • 75% of 0.08

    = 75/100 X .08 = .06

  • 161. When heated an iron bar expands 0.2%. If the increased length is 1 cm, what is the original length of the bar?

  • .02% is 1 cm

    1% is 1/.02

    100% is 100/.02 = 500cm

  • 162. Of the 3600 employees of ABC Ltd, 1/3 are clerical. If clerical staff were to be reduced by 1/3 what percent of the total number of the remaining employees would then be clerical?

  • Of the 3600 employees of ABC Ltd, 1/3 are clerical.

    Clerical Employees = 3600/3 = 1200

    If clerical staff were to be reduced by 1/3, Reduction =1200X1/3 = 400

    New Clerical Employees = 800

    New total employees = (3600-400) = 3200

    % = 800/3200 X100% =25%

  • 163. In a city 90% of the population own a car, 15% own a motorcycle, and everybody owns one or the other or both. What is the percentage of motorcycle owners who own cars?

  • In the question, it asked What is the percentage of motorcycle owners who own cars?

     

    % with both car and motorcycle = (90+15) - 100

                                                              = 5%
    % motorcycle = 15%
    now 5/15 = 1/3 = 33 (1/3) %

  • 164. If a length of a rectangle is increased by 30% and the width is decreased by 30%, then the area will be-

  • Let, x = original width

    and y = original length

    Then,

    Area = xy

     

    After change:

    width = x - 0.30x = 0.70x

    length = y + 0.30y = 1.30y

    Then,

    Area = (0.70x)*(1.30y) = 0.91xy

    Change in area:

    (xy - 0.91xy)

    =0.09xy

    Percent change in area:

    (0.09xy)/xy *100

    =0.09 * 100

    =9% decrease in area

  • 165. Which of the following fractions is the equivalent of 0.5%?

  • To change percent into fraction, take out the percent symbol and divide it by 100. 

    So, 

    0.5% becomes 0.5/100 

    Now, move the decimal place to the right in the numerator and the denominator until you have rid the fraction of decimals. 

    So, 

    0.5/100 becomes 5/1000 

    The number of times you move the decimal place in the numerator is equal to the number of zeros you add in the denominator. 

    Then reduce: 

    5/1000 = 1/200 

    (divide both numerator and denominator by common factor 5) 

  • 166. In a triangle the lengths of two sides are 5 and 9 and the length of the third side is represented by x. Which statement is always true?

  • If we let the side with length 9 as the largest side of the triangle, then 5 + x must be greater than 9 to form a triangle.

    Thus,  5 + x > 9

    or, x > 9 - 5

    or, x > 4

    If we let x be the largest side.

    Then, x must be less than 5 + 9

    So, x < 14

    Thus, by combining it, we get,

    4<x <14

  • 167. Zinat’s father contributes to his daughter’s saving by giving her 10% of her total saving. If Zinat saves Tk. 100 in June, Tk. 250 in july and Tk. 130 in August, how much will she have in savings (in Tk.) at the end of that time?

  • Total savings in June = 100 + (100 * 10 / 100) tk = 110 tk

    Total savings in July = 250 + (250 * 10 / 100) tk = 275 tk

    Total savings in August = 130 + (130 * 10 / 100) tk = 143 tk

    At the end of that time, she will have,

    110 + 275 + 143 tk = 528 tk

  • 168. What is the rate of discount if a car that had a regular price of Tk. 30,00,000 is sold for Tk. 27,90,000?

  • Discount amount = 30,00,000 - 27,90,000 tk

                               = 2,10,000 tk

    Thus,

    When original price is 30,00,000, discount is 2,10,000 tk

    When original price is 100, discount is 2,10,000 * 100 / 30,00,000 tk

                                                              = 7 tk

  • 169. 1 quintal 25 kg is what percent of 1 metric ton?

  • 1 Quintal = 100 kg

    1 Metric Ton = 1000 kg

    1 Quintal + 25 kg = 125 kg

    Now,

    So, percentage is = 125 * 100 / 1000

                                = 12.5% or 121/2%

  • 170. If A’s income is 25% less than that of B, then how much percent is B’s income more than that of A?

  • Let B's income be 100 X

    A's income is 25% less =  75 X


    B's Income / A's income = 100X / 75X = 4/3 = 133.33 %

    So, 33.33% or     331/3% more

  • 171. If the price of an item increases from Tk. 25 to Tk. 28, the old price is what % of the new price?

  • When new price is 28 tk, old price is 25 tk

    When new price is 100 tk, old price is 25*100/28 tk

                                                             = 89.29 tk or 89.29%

  • 172. If a 10% deposit that has been paid toward the purchase of a certain product is Tk. 110, how much more remains to be paid?

  • Let total price be p.

    10/100P = 110

    or, p = 110*100/10

            = 1100

    Now,

    1100 - 110 = 990

  • 173. A company increases every salary of an officer by 20%. His salary in the year 2001 was Tk. 26,640. What was his salary in 1999?

  • Let his salary in 1999 be x.

    In 2000, his salary increased into= 1.2x

    In, 2001, his salary increased into= 1.2 * 1.2x

                                                        = 1.44x

    Now,

    1.44x = 26640 tk

    or, x = 26640/1.44 tk

            = 18,500 tk

  • 174. If the radius of a circle is increased by 1%, l then the area of that circle increases by what percent?

  • Area of first circle= Pi*r2 

    Area of second circle= Pi*(1.01r)2 = Pi*1.0201r2

    Percentage increase = (Pi*1.0201r2 - Pi*r2 ) * 100 / Pi*r2 

                                     = (1.0201 - 1) * 100

                                     = 2.01%

  • 175. During a special promotion, a certain filling station is offering a 10% discount on gas purchased after the first 10 gallons. If Kim purchased 20 gallons of gas, and Zeni purchased 25 gallons of gas, then Zeni’s total per-gallon discount is what percent of Kim’s total per-gallon discount?
  • 176. If n = (79-6), what is the units digit of n?

  • 79 = 40353607

    Then,

    (79-6) = 40353607 - 6 = 40353601

    Unit digit means the first digit from the right.
    বাংলায় যাকে একক ঘরের সংখ্যা বলে।

    Here the unit digit is 1.

  • 177. Rahim’s convertible gets gas mileage that is 40% higher than that of Karim’s SUV. If Jalil’s hatchback gets gas mileage that is 15% higher than that of Rahim’s convertible, then Jalil’s hatchback gets gas mileage that is what percent greater than that of Karim’s SI V?
  • 178. A person makes a profit of 10% on 25% of the quantity and a loss of 20% on the rest. What is the percentage gain or loss on the whole?

  • If whole quantity is 100

    10% profit from 25% is = 25*110/100 = 27.5

    20% loss from 75% is = 75*80/100 = 60

    Total price of selling = 60 + 27.5

                                     = 87.5

    We can see that there has been a loss.

    Loss is = 100 - 87.5 = 12.5 or 12.5%

  • 179. In a survey, it was found that 65% of the people surveyed watched the news on television, 40% read it on newspaper, and 25% read a newspaper and watch the news on television. What percent of the people surveyed neither watched the news on television nor read a newspaper?
  • 180. In a college, 45% of the students are boys. If 40% of the boys and 20% of the girls’ went on a picnic, what percentage of the total students went to the picnic?

  • If total student is 100

    Then, boys are 45

    and girls are 55

    Now,

    40% of 45 boys is = 40*45/100

                               = 18

    And,

    20% of girls is = 20*55/100

                          = 11

    Thus, Total = 18 + 11 = 29 students went on the picnic

  • 181. Last year Asma bought two paintings. This year she sold them for BDT 2000 each. On one painting, she made 25% profit, and on the other painting she has 25% loss. What was he net loss or profit?

  • Total loss >BDT 200

  • 182. Sterling silver is 92.5% pure silver. How many grams of sterling silver must be mixed to a 90% silver alloy to obtain a 500g of a 91% silver alloy?
  • 183. The sale price of an article including the sales tax is Tk. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:

  • cost price=500
    then,in 12% profit,
    selling price=500 x 112/100=560 tk
    with 10% tax,
    price= 560+56=616 tk

  • 184. At what profit percent must an article be sold so that by selling at half that price, there may be a loss of 30%?

  • at 40% profit,
    if cost price 100 then selling price 140 tk
     half  of selling price =140/2=70
    then,
    loss=100-70/100x 100=30%
    so ,profit must be 40%
     

  • 185. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

  • profit=25-20/20 x 100%=25%

  • 186. 10% loss on selling price is what percent loss on the cost price?

  • 10% loss on selling income,
    cost=110
    sell=100
    now loss on cost=110-100/110=100/11%

  • 187. If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area?

  • p-q-(pq)/100=40-40-(40x40)/100=-16%

  • 188. In an examination, 34% of the students failed in Mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then the percentage of students who passed in both the subjects was:

  • here,
    failed only in math= (34-20)=14%
    failed only in english=42%-20%=22%
    total failed =14+22+20=56%
    passed=100-56=44%
     

  • 189. In a city, 40% of the people are illiterate 60% are poor. Among the rich, 10% are illiterate. What percentage of the poor population is illiterate?
  • 190. কংকা টিভির মূল্য ২০% হ্রাস করার ফলে যদি উহার বিক্রয়ের পরিমান ৫০% বৃদ্ধি পায়, তাহলে কোম্পানির বিক্রয় খাতে অর্জিত রাজস্ব আয়ে পরিবর্তনের হার কিরুপ হবে? 

  • ১০০×(৮০/১০০)×(১৫০/১০০)

    =২০%

  • 191. একটি ব্যাংকের একটি ব্রাঞ্চের 60% কর্মচারী পুরুষ। যদি কর্মচারীদের মধ্যে 70% পুরুষ এবং 90% মহিলা বনভোজনে অংশগ্রহণ করে, তবে ব্রাঞ্চের কর্মচারীদের কত শতাংশ বনভোজনে অংশগ্রহণ করে? 

  • ৬০% কর্মচারী পুরুষ হলে মহিলা কর্মচারী রয়েছে (১০০-৬০) বা ৪০%

    পুরুষের ক্ষেত্রে,

    ১০০ জন পুরুষের মধ্যে বনভোজনে গিয়েছে ৭০ জন

    ৬০ জন পুরুষের মধ্যে বনভোজনে গিয়েছে ৭০*৬০/১০০ জন

                                               = ৪২ জন

    মহিলার ক্ষেত্রে,

    ১০০ জন মহিলার মধ্যে বনভোজনে গিয়েছে ৯০ জন

    ৪০ জন মহিলার মধ্যে বনভোজনে গিয়েছে ৯০*৪০/১০০ জন

                                               = ৩৬ জন

    সুতরাং, মোট ১০০% কর্মচারীর মধ্যে যাচ্ছে (৪২+৩৬)% বা, ৭৮%

  • 192. In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?     
  • Let +a+ = quantity of 20% solution needed ( in any units )
    Let +b+ = quantity of 50% solution needed ( in the same units )
    +.2a+ = alcohol in 20% solution
    +.5b+ = alcohol in 50% solution
    given:
    +%28+.2a+%2B+.5b+%29+%2F+%28+a+%2B+b+%29+=+.4+
    +.2a+%2B+.5b+=+.4%2A%28+a+%2B+b+%29+
  • 193. A 6% stock yields 8%. The market value of the stock is :

  • For an income of BDT 8, investment = BDT 100.

    For an income of BDT 6, investment = BDT (100/8 X 6) = BDT 75

  • 194. A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are:

  • student got 125 marks and failed by 40
    pass marks = 165
    33%=165
    so,100%=165 x100/33=500 mark

  • 195. 125 gallons of a mixture contains 20% water. What amount of additional water should be added such that the water content is raised to 25%

  • Let, x gallons water should be added.

    Here, 125 gallons of a mixture contains 20% water is (125× 20/100)= 25 gallons

    According to the question,

    25+x = (125+x)×25/100

    => 25+x = (125+x)×1/4

    => 4(25+x) = 125+x

    => 100+4x = 125+x

    => 4x-x=125-100

    => 3x=24

    => x=24/3

    So, x=81/3

    So, 81/3 gallons water should be added. (Ans.)

  • 196. কোন পরীক্ষায় ৫২% পরীক্ষার্থী ইংরেজীতে এবং ৪২% গণিতে অকৃতকার্য হয়। যদি ১৭% পরীক্ষার্থী উভয় বিষয়ে অকৃতকার্য হয়, তবে কতজন পরীক্ষার্থী উভয় বিষয়ে কৃতকার্য হয়েছিলো?  

  • ইংরেজীতে ফেল করে= (৫২-১৭) জন=৩৫ জন
    গনিতে ফেল করে= (৪২-১৭)%=২৫ জন
    পাশ করে ={১০০-(৩৫+২৫+১৭)} জন=২৩ জন
    পাশ করে ২৩%

  • 197. কাগজের পূর্বমূল্য : বর্তমান মূল্য= 2:3, পূর্বের তুলনায় কাগজের মূল্য শতকরা কত বৃদ্ধি পেয়েছে?  

  • কাগজের পূর্ব মূল্য=২ক
    কাগজের  বর্তমান মূল্য=৩ক
    বৃদ্ধি =(৩ক-২ক)=ক
    ২ক  টাকায় এ বৃদ্ধি পায় ক টাকা
    ১  টাকায় এ বৃদ্ধি পায় ক/২ক টাকা
    ১০০  টাকায় এ বৃদ্ধি পায় ১০০ x ক/২ক টাকা=৫০ টাকা

  • 198. A town has a population growth rate of 10% per year. The population in 1990 was 2000. What was the population in 1992?

  • In 1991, population is,

    110% of 2000 is = 2000*110/100

                           = 2200

    In 1992, the population is,

    110% of 2200 is = 2200*110/100

                            = 2420

  • 199. After being marked down 20 percent, a calculator sells for Tk. 10. The original selling price was-

  • 20% down means 80% of original price.

    Thus,

    80% of original price is 10 taka

    100% of original price is = 10*100/80 taka

                                      = 12.5 taka

  • 200. In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2:3, then what percent of the population is literate?
  • 201. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

  • Let C.P.= BDT 100. Then, Profit = BDT 320, S.P. = BDT 420.

    New C.P. = 125% of BDT 100 = BDT 125

  • 202. In an election between two candidates, one got 55% of the total valid votes. 20% of i the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was-

  • Number of valid votes = 80% of 7500 = 6000.

    Valid votes polled by other candidate = 45% of 6000

    = (45X6000/100)% = 2700

  • 203. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percentage; increase of the population per year is-

  • Increase in 10 years = (262500 - 175000) = 87500.

    Increase% = (87500X100/175000)% = 50%

    Required average =50/10%=5%

  • 204. What percentage of numbers from 1 to 70 has 1 or 9 in the unit’s digit?

  • Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

    Number of such number =14

    Required percentage =(14/70 X 100) %= 20%.

  • 205. A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2500 gallons of water evaporate from the tank, the remaining solution will be approximaiely what percent sodium chloride?

  • Original =10,000 ----> sodium chloride = 5% ie 500
    New = 10,000-2,500 = 7500.

    New % = (500/7500) * 100

    = 6.67%

  • 206. The price of apple in the year 2010 has increased by 15% from that of the previous year. In 2011 the price has decreased by 10%. In 2011, what was the increase in price with respect to that of 2009?
  • 207. A 20% reduction in price allows a customer to purchase 5 kgs of rice at Tk. 160. How much would have to pay if there was no discount?

  • 20% discount means, 80% of the original price.

    Thus,

    80% = 160

    100% = 160*100/80

                = 200 tk

  • 208. In a horticulture experiment,-200″ seeds were planted in plot I and 300 were planted in plot II. If 57 percent of the seeds in plot I germinated and 42 percent of the seeds in plot II germinated, what percent of the total number of planted seeds was germinated?

  • Total seeds = 200 + 300 = 500

    57% of 200 = 200*57/100 = 114

    and, 42% of 300 = 300*42/100 = 126

    Total Germinated seeds = 126 + 114 = 240

    % of germinated seeds = 240*100/500

                                                = 48

  • 209. A group of students decided to collect as many paisas from each member of a group as is the number of members. If the total collection amounts to Tk. 59.29, what is the number of members in the group?

  • Money collected = (59.29 x 100) paise = 5929 paise.

    Number of members = 5929 = 77.

  • 210. A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 percent larger than the original. By what percentage has the area of the logo increased?

  • The area goes up as the square of the diameter, so the new area is (1.5)^2 times the old area, = 2.25 times larger.

    But the question is about the increase. The increase is 125%

  • 211. 60% of the students of a college are male. 60% of the males in the college speak French and 40% of the students of the college speak French. What is the percentage of the females in the college who do not speak French?
  • 212. 0.01 is what percent of 0.1?

  • .01=x/100 × .1

    x=10

  • 213. An article when sold at a gain of 5% yields Tk.15 more than when sold at a loss of 5%. Its cost price would be:

  • difference =(105-95)=10

    cost price=(100×15)/10

                       =150

  • 214. Jesmin spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had 500 left over. How much money did she start with?
  • 215. In the last week of a month, a car dealer sold 12 cars. A new sales promotion came out the first week of the next month and he sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?
  • 216. A salesman usually makes 25% profit on every radio he sells. During a sale, he reduces his profit margin to 20%, while his sales increases by 10%. What is the ratio of his new profit to his usual profit?
  • 217. An instrument store gives a 10% discount to all students of original cost of an instrument. During a school sale an additional 15% is taken off the discounted price. Rahim, a student at the local high school, purchased a flute for Tk. 306. How much did it originally cost?
  • 218. A chair costs Taka 24,050 after 7.5 percent discount. What was its catalog price?
  • 219. A taxi charges Taka 50 for the first 2 kilometers and Taka 20 for each additional kilometer. How much would be the fare for 32 kilometers?
  • 220. A hammer and a screwdriver currently have the same price. If the price of a hammer rises by 6% and the price of a screwdriver goes up by 4%, how much will it cost to buy a hammer and screwdriver?

  • SD = 100
    H = 100

    SD +  H = 200

    After increase

    SD = 104
    H = 106

    SD +  H = 210

    % increase = (210 - 200)/200 * 100 = 5 %

  • 221. In a certain city 40% of the people have black hair, 25% have black eyes and 10% have both black hair and black eyes. What percentages of the people in the city have neither black hair nor black eyes?

  • Only have black hair = (40 - 10) = 30%

    Only have black eyse = (25 - 10) = 15%

    Thus, Percentage of people in the city who have neither black hair nor black eyes = (100 - 30 - 15 - 10)% = 45%

  • 222. In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many marbles will he have to take out of his pocket to ensure that he has taken out at least one of each color?

  • In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. 

    If he takes out 3 balls, they can all be red.

    If he takes out 4 balls they can all be green or blue.

    if he takes out 7 balls they can all be red and blue.

    if he takes out 8 balls they can all be green and blue.

    but if he takes out 9 balls, he must have balls from each color

  • 223. The population of Barisal is 50 percent of the population of Chittagong. The population of Barisal is what percent of the total population of Barisal and Chittagong?

  • Population of Chittagong = 100

    Population of Barisal = 50

    Population of Barisal and Chittagong = 100 + 50 = 150

     

    Thus,

    Percentage of Population of Barisal against Population of Barisal and Chittagong = 50*100/150

                          = 331/3%

  • 224. In the last week of a month, a car dealer sold 12 cars. A new sales promotion came out in the first week of the next month and he sold 19 cars during that week. What was the percent increase in sales from the last week of the previous month to the first week of the next month?
  • 225. The selling price of 15 items equals the cost of 20 items. What is the percentage profit earned by the seller?

  • 20-15= 5 item

    So,the percentage profit earned is 5/15x100=33.3%

  • 226. In 2007, the arithmetic mean of the annual incomes of Rahim and Karim was Taka 3800. The arithmetic mean of the annual incomes of Karim and Ripon was Taka 4800, and the arithmetic mean of the annual incomes of Ripon and Rahim was Taka 5800. What is the arithmetic mean of the incomes of the three?

  • (Rahim+karim)/2+(Karim+ripon)/2+(Ripon+Rahim)/2=3800+4800+5800

    So, (Rahim+Karim+Ripon)/3=14400/3=4800

  • 227. In a country, 60% of the male citizen and 70% of the female citizen are eligible to vote. 70% of male citizens eligible to vote voted, and 60% of female citizens eligible to vote voted. What fraction of the citizens voted during the election?

  • Let, male =x , female=y

    Male voted=x × 60/100  ×70/100

                     =42x/100

    Female voted=y ×70/100 ×60/100

                       =42y/100

    So, fraction of citizen voted= (42x/100  × 42y/100)/x+y

  • 228. The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?

  • (100x25)/125

    =20

  • 229. In an election a candidate who gets 84% of the votes of the votes is elected by a majority of 476 votes. What is the total number of votes polled?

  • The question doesn't mention that it has only another candidate. If there was only one candidate he got 16%

    Difference between them, 68%

    68% =476; 100% = 700

    But otherwise there is no correct answer.

  • 230. The total income of Mr. Sakib in the years 2003, 2004, and 2005 was Taka 36,400. His income increased by 20% each year. What was his income in 2005?

  • Income in 2003=x

    Income in 2004 =.20x+x

    income in 2005=(x+.20x)+.20(x+.20x)

    Now,x+.20x+x+x+.20x+.20x+.04x=36400

    x=10000

    income in 2005=14400

     

  • 231. Successive discount of 20% and 25% are equal to want single discount rate (%)? 
  • 232. Out of total profit, A gets 40%, B 25%, C 20%, D 10% and E 5%. A’s profit is what percentage of that of B? 

  • A’s profit in percentage of that of B = 40*100/25 = 160%

  • 233. A portion of TK 7200 is invested @4%, and the rest is invested @5% annual return. If the annual income from both the portion is same, what is the total income from investment? 
  • 234. The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?
  • 235. Every 3 minutes, 4 liters of water are poured into a 2,000-litre tank. After 2 hours, what percent of the tank is full?
  • 236. If w is 10% less than x, and y is 30% less than z, then wy is what percent less than xz?
  • 237. Bus fare recently was increased from Taka 0.85 to Taka 1.00. What was the approximate percentage of increase?
  • 238. Which of the numbers below is not equivalent to 4%?
  • 239. A 5% monthly salary increase resulted in a salary increase of Tk. 6000 per year for an employee. What was his monthly salary before the increase?
  • 240. There are 900 students in a school. 4% of them left the school and 50% of the remaining is girls. How many girls remained?

  • 4% of 900 students is= 900*4/100 = 36 students

    Thus, remaining student number is= 900-36 = 864

     

    50% of the remaining is Girls.

    Thus, Total number of number of Girls is= 50*864/100

                                                            = 432

  • 241. The price of sugar is increased by 10%. What % of consumption of sugar is to be reduced in order to keep the expenditure on sugar at the same level?
  • 242. The cost of the carriage and the horse is Taka 1500 and Taka 2000 respectively. If the cost of carriage increases by 5% arid the cost of horse increases by 8%. The total cost of the carriage arid the horse (in Taka) would be--

  • 5% increase in cost of Carriage means cost of carriage

    = 1500*105/100 tk

    = 1575 tk

    8% increase in cost of Horse means cost of Horse

    = 2000*108/100 tk

    = 2160 tk

     

    Total cost of Carriage and Horse = (1575 + 2160) tk

                                                   = 3735 tk

  • 243. What was the original price of a pen (in Taka) if it is bought for Tk. 100 at 20% discount?

  • 20% discount means (100 - 20) or, 80% of original price.

    Thus,

    80% of the original price is 100 tk

    100% of the original price is 100/.8 tk

                                           = 125 tk

  • 244. If a=-1, then, (a4+a3+a2+a)=

  • (a4+a3+a2+a)

    = [(-1)4+(-1)3+(-1)2+(-1)]

    = (1-1+1-1)

    = 0

  • 245. Per day wage rate of workers is reduced 50% due to economic slowdown. After one year, the wage rate is increased by 60%. If the per day wage rate before the decrease was TK. 100, then what is the per day wage rate now? 
  • 246. Out of total profit, A gets 40%, B 25%, C 20%, D 10% and E 5%. A’s profit is what percentage of that of B? 

  • Let total profit be 100,

    Then, A gets 40,

    B gets 25,

    Percentage of A's profit of that of B is = 40*100/25

                                                            = 160%

  • 247. A man buys tk 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:

  • Dividened of tk 20 = tk (20x 9/100) =tk 9/5

    an interest of 12%,

    he gets tk 12 from 100 tk

    he gets 9/5 tk from 100*9/(5*12) tk =15

  • 248. In a survey of the people in Dhaka, it was found that 65% of the people surveyed watched the news on television, 40% read newspaper, and 25 read a newspaper and watched the news on television. What percent of the people surveyed neither watched the news on neither television nor read a newspaper? 
  • 249. If 18 is 15 percent of 30 percent of a certain number what is the number?
  • 250. The organizers of a fair projected a 25% increase in attendance this year over that of last year, but attendance this year actually decreased by 20%. What percent of the projected attendance was the actual attendance? 
  • 251. At an election involving two candidates, 68 votes were declared invalid the winning candidate secures 52% and wins by 98 votes. The total numbers of votes polled is: 

  • suppose,
    required number of votes=x
    valid votes=(x-68)
    here,
    (x-68) x 52/100-(x-68)x48/100=98
    so,x=2518

  • 252. Number 29 is 10 percent of what number?

  • 10% of the number is 29

    100% of the number is 29*100/10

                                        = 290

  • 253. What is 1 percent of 0.025?

  • 0.025*1/100

    = 0.00025

  • 254. 10 percent of 4800 is how much more than 8% of 4800?

  • 100% is 4800

    1% is 4800/100 = 48

     

    Difference between the percents is = (10-8)% = 2%

    Thus,
    2% is 48*2 = 96
     

  • 255. The selling price of 8 apples is equal to the purchase price of 10 apples? What is the profit margin?

  • Selling price of 8 apples be 100

    Then, Purchasing price of 10 apples is 100.

    Now,

    Selling price of 8 apples be 100

    Selling price of 10 apples be 100*10/8 = 125

    Profit margin = (125-100)% = 25%

  • 256. একটি দ্বীপের লোকসংখ্যা ৬৫০৬৫০ । ঘূর্নিঝড়ে ঐ দ্বীপের ২০% লোক নিহত হয়। ঘূর্নিঝড়ের পর দ্বীপের লোকসংখ্যা কত হল?

  • বীপের ৮০% লোক = ৬৫০৬৫০*৮০/১০০ = ৫২০৫২০

  • 257. একটি বাক্সে লাল অ সবুজ রঙ্গের কিছু বল আছে। এতে ৪০% বল লাল এবং বাকি বলগুলো সবুজ। আকৃতির দিক দিয়ে বাক্সের অর্ধেক সংখ্যক বল ছোট এবং অর্ধেক সংখ্যক বল বড়। ১০% বল লাল ও ছোট এবং ৩০টি বল সবুজ ও বড়। বাক্সে মোট কতগুলো বল আছে? 

  • সবুজ বল = ক - ০.৪ক = ০.৬ক

    ছোট বলের মোট সংখ্যা= .০.৫ক

    বড় বলের মোট সংখ্যা= .০.৫ক

    লাল ছোট বল = ০.১ক

    সুতরাং, লাল বড় বল = .০.৪ক - ০.১ক = ০.৩ক

    এখন,

    বড় বল অবশিষ্ট থাকে = ০.৫ক - ০.৩ক = ০.২ক

    প্রশ্নানুসারে,

    ০.২ক = ৩০

    বা, ক = ৩০/০.২ = ৩০০/২ = ১৫০

  • 258. A student multiplied a number by 3/5 instead of 5/3. What is the percentage of error in the calculation?

  • Error %= error / true value

    but, here.. error= true value-false value

    ie., error=(5/3)-(3/5)=16/5

    so the error % will be equal to (16/5)/(5/3)=64%

    (since, true value is 5/3)

  • 259. The market value of a 10.5% stock, in which an income of Tk. 756 is derived by investing Tk. 9000, brokerage being ¼%, is:
  • 260. If selling price is doubled, the profit triples. Find the profit percent.

  • profit = S.P -C.P
    S.P = 2Y
    C.P = X
    PROFIT = 3(Y-X)= (2Y-X)
    = 3Y-3X-2Y+X
    = 1Y-2X
    (i.e)Y=2X : Profit = (Y-X)(i.e) =(2x-x)=Rs.x
    Profit% = C.P/profitX100= X/X*100=100%

     

     

  • 261. If a man’s salary is 20% more than that of his son, how many percent is the son’s salary if compared to the salary of his father?

  • When son's salary is 100, that of father's is 120

    Reversibly,

    When father's salary is 120, that of son's is 100

    and, When father's salary is 100, that of son's is 100*100/120

    = 83.34 %

  • 262. A toy was bought for tk. 75 and sold at a gain 8%. What was its selling price in tk?

  • When Buying price 100 tk, selling price 108 tk

    When Buying price 75 tk, selling price 108*75/100 tk

                                                               = 81 tk

  • 263. 8% of 0.06 = ?

  • 0.06*8/100 =  0.0048

  • 264. In a group of people solicited by a charity, 30% contributed tk. 40 each, 45% contributed tk. 20 each and the rest contributed tk. 12 each. What percentage of the total amount came from people who gave tk. 40 each?

  • 30% contributed=40×30%=12 Tk

    45% contributed=20×45%=9 tk

    Rest={100-(30+45)}%=25% contributed= 3 tk

    total=12+9+3=24

    The percentage of the total amount came from people who gave tk. 40 each=(12×100)/24=50%

     

  • 265. 75% of students of a class answered question No.1 correct and 55% answered Question No.2 correct and 20% answered neither question correctly. What percent of students answered both questions correctly?

  • Students answered Q.-1 or Q.-2 or both correctly = (100-20) = 80% 

    Let, x% students answerd both correctly. 

    .:. (75-x) + (55-x) + x = 80 

    130-x = 80 

    .:. x= 50

  • 266. The organizers of a fair projected 25% increase of visitors this year over that of the last year but the actual turnover was 20% less than that of last year. What persent of projected visitors attended the fair?

  • Let,last year visitor=100

    projected visitor=100+25=125

    Actual visitor=100-20=80

    % of Attended visitor=80/100x100%=64%

  • 267. The price of corn rose 20% two years ago and 15% last year. What is the combined persent increase in price?

  • combined persent increase in price=p+q+pq/100

    =20+15+(20x15)/100

    =38

  • 268. Riaz spent 20% of his income on taxes and 20% of the remainder on rent. What persent of his income has he spent on rent?

  • Remain = (100-20)% = 80%

    Spent on rent = 20% of 80% 

    = 20/100 X 80%

    =16% 

  • 269. If price of oil is increased by 331/3%, by how much a housewife must reduce consumption of oil so that her expenditure on oil remains the same?

  • If price of x amount oil was 100

    Then, now it is 100+331/3 = 1331/3

    Housewife used to spend 100 for x amount of oil.

    1331/3  is the price of x amount

    100 is the price of x*100/1331/3 

                                = x*100*3/400

                                = 3x/4

    Must reduce (x- 3x/4)

                       = (4x-3x)/4

                       = x/4

        &nbs

  • 270. If A’s salary is 110% of B’s, B’s salary is 80% of C’s, find C’s salary, if A’s salary is Tk. 440.
  • 271. A fruit seller sells 30% apples and still has 630 apples in the stock.How many apples had he bought ?
  • 272. In an examination, a student has to secure 40% marks to pass. One student got 40 marks and failed by 40 marks. What was the total marks in the examination?   
  • 273. If rate of income tax is increased from 20% to 25% find the additional amount of tax a person has to pay. if his total income is tk 40,000 ?
  • 274. Per day wage rate of workers is reduced 50% due to economic slowdown. After 1 year, the wage rate is increased by 60%. If the per day wage rate before the decrease was tk.100 , then what is the per day wage rate now?

  • When reduced, 100 - 50 = 50 

  • 275. In redesigning a cold storage, the length is increased by 30%, the breadth is increased by 50% and the height is reduced by 20%. What is the next increase In the volume of the redesigned cold storage compared to the previous design?

  • Shortcut=

    %C=|100-(130x150x80)/100x100|

         =56

  • 276. You can now buy 5 more mangoes with tk 75 due to reduction is price by 20 percent. Calculate the current price of one dozen of mangoes ?

  • price reduction is 20 percent

    Old price 100, current price 80

    Old price 75, current price 80/100 * 75 = 60 TK

    So, 5 mangoes current price is (75-60) = 15 TK

    Current price of 1 dozen = 36 TK

  • 277. What percent of 25 is 0.20 ?

  • P/100x25=.20

    25P=20

    P=.8

  • 278. Alam spent 30% of his income on taxes and 20% of the raminder on rent.what per cent of his income he has on rent ?

  • (100-20)×20%

    =80(20/100) = 16 (Ans.)

  • 279. After paying 10% tax on all income over tk 3000.Rahim had a net income of tk 12000, Rahims income before tax was-

  • 12,000-3,000 = 9,000

    10% tax, if after tax income Tk. 90 before tax income Tk. 100

            "      "      "        "        "      Tk. 9,000  "       "     "        = Tk. (100×9000)/90

                                                                                   &nbs

  • 280. There were twice as many as boys in a class. If 30% of the girls and 45% of the boys have already handed over their reports, what percent of the students have not yet done so?  

  • Let, Boys = 100, Girls = 200

    200×30% + 100×45% = 60+45 = 105

    {(300-105)/300}×100% = (195/300)×100% = 65% Ans.

  • 281. The price of a loaf of bread increased by 20%.How many loaves can be purchased now by the amount of money used to buy 300 loaves at the earlier price?    

  • Let, earlier cost price of 1 loaf is Tk. x

    So, Earlier cost price of 300 loaves is 300x

    At 20% increase, x+x × 20% = 1.2x

    Now, 300x/1.2x = 250 (Ans.)

  • 282. The price of sugar increased by 10%. What % of consumption of sugar is to be reduced in order to keep the expenditure on sugar at the same level?    

  • 10% increase,

    New price will be Tk. 110 if old price is Tk. 100

    So,   "   "    "    "      1    "     "      "      100/110

    So,   "   "    "   "     100    "     "      "    (100×100)/110 = 90.91

    So, 100-90.91 = 9.09

  • 283. 68% of the candidates in a recruitment test have passed the written part of it. The number is 14 less than what would have been in case 75% would have passed. What was the number of candidates appeared?   

  • 75% - 68% =7%

    7%=14

    So, 100%= (14×100%)/7% = 200

  • 284. There are 900 students in a school 4% of them left the school and 50% of the remaining are girls.how many girls remained in the school ?  

  • 900×(4/100)=36

    Remaining = 900-36 = 864

    Girls = 864/2 = 432

  • 285. One-half of the employees of a company earns over Tk. 18000 per month. One-third of the remainder earns between Tk. 15000 and Tk. 18000. What part of the staff earns below Tk. 15000?  

  • 1/2 + 1/2 × 1/3

    = 1/2 +1/6

    = (3+1)/6

    = 4/6

    =2/3

    So, 1 - 2/3

    =1/3 (Ans.)

  • 286. The population of a country doubled every 10 years from 1980 to 2010. What was the percent increase in population during the period?  
  • 287. What percent of 50 is 2?

  • 50 X x% = 2

    =>50 X x/100 = 2

    => 4

  • 288. An ore contains 26% of copper,to get 91kgs of copper the quantity of are required is
  • 289. Mr. Khan’s salary is Tk. 5000 and he gets 10% commission of his salary. If his salary increased by 10%, by what percent his commission will increase?
  • 290. Novera brought a ticket of cricket match for tk. 25 and later sold the ticket to Nahid for Tk. 75. What was the percent increase in the price of the ticket?
  • 291. if 150 is increased by60% and then decreased by x percent, the result is 192. what is x?  
  • 292. if 75% of a number is added to 75. then the result is the number itself .  The some of the number is  

  • here,
    75% of x plus 75 = x
    0.75x + 75 = x
    Bring the variable terms to the left side of the equation by subtracting x from both sides.
    -0.25x + 75 = 0
    Bring the constant terms to the right side by subtracting 75 from both sides.
    -0.25x = -75
    Divide both sides by -0.25
    x = 300

     

  • 293. A sum of money invested at compound interest amounts to Rs 4624 in 2 yrs and Rs 4913 in 3 yrs. The sum of money is  

  • Explanation:
    4913 = P [1 + r/100]3
    4624 = P [1 + r/100]2
    Divide both equations, find r
    Put value of r in one of the equations to find P

  • 294.  If   tk 64 amount to 83.20 in 2 years what will tk 86 amount  to in  4 years in the same rate percent per annum?  

  •  Let ,
     P=Taka 64,  S.I. = Taka (83.20 - 64) = Taka 19.20, T = 2 years
    So, rate = ( 100 x 19.20 )/ (64 x 2) % = 15%
    Now, P = Taka 86, R= 15%, T = 4 years
    S.I. =  Taka ( 86 x 15 x 14 )/100= Taka 51.60

  • 295. In an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?  

  • Let the total number of votes polled be x.

    Then, votes polled by other candidate = (100 - 84)% of x = 16% of x.

    ∴
     84% of x - 16% of x = 476

    or,(68/100)x =476

    so,x=700 (Ans) 

  • 296. A towel , when bleached was found to have lost 20% of its length and 10% of its breadth . The percentage of decrease in area is :  

  • Suppose ,

    a number is decreased by =x%  and then again decreased by length  =y%
    Then,

    net change  ={−x−y+(xy/100)} % = 28%

  • 297. Q  In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B . The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in the election ?  

  • Let the number of persons eligible to vote be x.

    Then,

    voters who voted for A = 30% of x.

    Voters who voted for B = 60% of (70% of x).

                                             =  42% of x
                                             =(60100∗70100∗100)% of x

                                              = 42% of x.

    Voters who did not vote = [100 - (30 + 42)]% of x = 28% of x.

    ∴ 30% of x - 28% of x= 1200

    => 2% of x= 1200

    => x = {1200 X (100/2)} =60000.

  • 298. 50% of a% of b is 75% of b% of C. Which of the following is C ?  

  • 50% of a% of b = b*50/100*a/100 = ab/200
    Again 75% of b% of C = C*75/100*b/100 = 3bC/400
    Now, ab/200=3bC/400 or, a =3C/2 or 3C = 2a or C =2a/3 So, 
    C = 0.667a

  • 299. Waht is the original price of a t-shirt, if the sale price after 15% discount is 272?
  • 300. If 61% of Bangladeshi people like coffee and 74% like tea, how many like both?
  • 301. If y% of x=29, then x=?
  • 302. 300 টাকার 4 বছরের সরল মুনাফা ও 400 টাকার 5 বছরের সরল মুনাফা একত্রে 160 টাকা হলে শতকরা মুনাফার হার কত?
  • 303. কোনো পরীক্ষায় মোট পরীক্ষার্থীর ৮০% গনিতে এবং ৭০% বাংলায় পাস করলো। উভয় বিষয়ে পাস করলো ৬০%, উভয় বিষয়ে শত করা কতজন ফেল করলো?
  • 304. ৪ টাকায় ৫টি করে আম কিনে ৫ টাকায় ৪ টি করে বিক্রয় করলে শতকরা কত লাভ হয়?
  • 305. ১/২ এর শতকরা কত ৩/৪ হবে?
  • 306. ধানে চাল ও তুষের অনুপাত ৭ঃ৩ হলে শতকরা কী পরিমাণ চাল আছে?
  • 307. 1/2 is what percent of 1/3?
  • 308. If w is 10% less than x and y is 30% less than z , then wy is what percent less than xz ?
  • 309. At a symposium  , 20 % of the professors are psychologists , 60% are biologists , and the remaining 12 professors are economists . If 20 of the professors were glasses , what present of the professors do not wear glasses ?
  • 310. ২% এর ভগ্নাংশ কত?
  • 311. যদি ১০০০ টাকার উপর ৬ মাসে লাভ হয় ৬০ টাকা, তবে লাভের শতকরা হার কত?
  • 312. বার্ষিক শতকরা ৭% হারে লাভে কত টাকা জমা দিলে ১৮ মাস পরে ১০০০ টাকা হবে?
  • 313. If x=80%, by what percent is x larger than x^2 ?
  • 314. The length of a rectangle is twice than that of its breadth. If the length of the rectangle is increased by 10%, while its breadth is decreased by 10% what is the percentage change in the perimeter ?
  • 315. Halim purchased brand A pen for Taka 200 each and brand B per for Taka 100 each. If he purchased a total of 8 of these pens for Taka 1,200 how many pens of brand A did he purchased ?
  • 316. What percentage of numbers from 1 to 70 has 1 or 9 in the unit digits ?
  • 317. In a class 75% passed in English, 60% in Mathematics and 25% failed in both the subjects. What is the percentage who passed in both subjects?
  • 318. A person makes a profit of 10% on 25% of the quantity and loss of 20% on the rest of the quantity. What is the gain or loss is percentage on the whole?
  • 319. Increasing the original price of an item by 10%, then decreasing by 20% and then again increasing the price by 10% is equivalent to :
  • 320. A dishonest shopkeeper professes to sell ghee at his cost price. But he uses a false weight of 950g for a kilogram. His gain percentage is :
  • 321. If x is 90% of y then what percent of x is y?
  • 322. If the cost price is 25% of selling price then what is the profit percent?
  • 323. A shopkeeper purchases 70kg of potatoes for Tk. 420 ans sold the whole lot as the rate of Tk. 6.50 per kg. What will be his gain in percentage ?
  • 324. A company generated revenue of Tk 125,000 in 2012 which was 12.5% o its gross revenue. In 2013, the gross revenue increased by Tk. 250,000. What is the percentage increase in the revenue in 2013?
  • 325. The price of a certain stock increased by 0.25 of 1 percent on a certain day. By what fraction did the price of the stock increase that day? 
  • 326. In a shipment of 120 machine parts, 5% were defective. In a shipment of 80 machine parts, 10% were defective. For the two shipments combined, what percent of the machine parts were defective?
  • 327. যদি কোন বর্গফলের প্রত্যেক বাহুর পরিমাণ ১০% বৃদ্ধি পায়, তবে তার ক্ষেত্রফল শতকরা কত বৃদ্ধি পাবে? 
  • 328. The income of 'A' is 20% higher than that of 'B' The income of 'B' is 25% less than of 'C’. What percent less is A's income from C's income
  • 329. When Mr X imported a certain item, he paid a 7 percent import tax on the portion of the item in excess of tk. 1000. If the amount of the import tax that Mr. X was tk. 87.50, what was the cost of the item? 
  • 330. What is 10% of y/3 if 2y/3 is 10% of 400? 
  • 331. If an organization increases its staff salary by 25%, by what percent must it now decrease to return to the original amount?
  • 332. In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subject. 
  • 333. The ratio of boys and girls in a school is 3:2. 20% of boys and 25% of girls are scholarship holders. The percentage of students who are scholarship holders are  
  • Total no of students = 100
    Boys = 100×(3/5) = 60
    Girls = 100- 60 = 40
    scholarship holders = (20% of 60 + 25% of 40) = (12+10) = 22 = 22%
  • 334. Pintu spent 20% of his income on taxes and 20% of the remainder on rent. What percent of his income has been spent on rent? 
  • Let,
    Income = 100 tk
    Spent on tax = 20 tk
    Spent on rent = 20% of (100-20) = 16 = 16%
  • 335. If the length and width of a rectangle garden plot were each increased by 20%, what would be the percent increase in the area of plot?  
  • Original area = LW
    Both are increased by 20%
    New area = 1.2L × 1.2W = 1.44LW
    % increase = {(1.44LW-LW)×100}/LW = 44%
  • 336. If an organization increases its staff salary by 25%, by what percent inust it now decrease the salary to return to the original salary?
  • % decrease = (125-100)×100/125 = 20%
  • 337. If it is 300 km from Dhaka to Chattogram and 180 km from Dhaka to Cumilla. What percentage of the distance from Dhaka to Chattogram is the distance from Dhaka to Cumilla?
  • x% of Dhaka to Chattogram = Dhaka to Cumilla
    Or, x% of 300 = 180
    Or, x= (180×100)/300
    Or, x = 60
  • 338. What is 1 percent of 0.025?
  • x is 1% of 0.025
    Or, x = (1/100) × 0.025
    Or, x= 0.00025
  • 339. কোনাে শহরের বর্তমান জনসংখ্যা ৪ লক্ষ। শহরটির জনশংখ্যা বৃদ্ধির হার শতকরা ২৫ জন হলে ২ বছর পরে শহরের জনসংখ্যা কত হবে?
  • 340. একজন কর্মচারির বেতন ২০% বৃদ্ধির পর সাপ্তাহিক ১৮০ টাকা পেল। তার আগের সাপ্তাহিক বেতন কত ছিল? 
  • 341. A milkman purchases the milk at Tk. x per liter and sells it Tk. 2x per liter still he mixes 2 liters water with every 6 liters of pure milk. What is the profit percentage? 

  • Let,
    He purchases 6liters milk.
    So, cost of 6 liters = 6x tk.
    After mixing 2 liters waters, he sells , (6+2)= 8 liters

    Now, selling price of 8 liters = 8 × 2x = 16x tk.
    Profit = 16x – 6x = 10x tk.
    Profit percentage = (10x/6x) × 100 = 166.66%

  • 342. If x is 30% greater than y, what percent of y is x?

  • if, y = 100 then x = 100 + 30 = 130

    then, x is 130% of y

  • 343. Bus fares were recently increased from Taka 1.70 to Taka 2.00.What was the approximate percentage of increase 
  • Bus fares increased 
=(2.00 -1.70)
=.30
in 1.70 Taka increase 
=.30 Taka =.301.70
 '. " 100   "    "    " .30×1001.70
=17.64 " 
=18%
  • 344. which of the numbers below is not equivalent to 20% 
  •  0% means =20100=15
or,  0.2 এগুলো অপশনে আছে
.'. not equivalent =0.5
  • 345. A shopkeeper gains 17% after allowing a discount of 10% on the marked price of an article. Find his profit percent if the article is sold at marked price allowing no discount. 

  • Let the cost price = 100

    Therefore, Selling price = (100×117)/100=117

    Therefore, Marked price = (117×100)/90=130

    Therefore, Profit Percentage = {(130−100)/100}×100=30%

  • 346. The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

  • Let price of book = 100tk

    Price of pen = 100+100×25% = 125 tk

    Price of penholder = 100 + 100×50% = 150 tk

    Difference is = 150 -125 = 25 tk

    Percentage = (25×100)/125 = 20%


today's words

Current World

  • What is the number of current U.S. Congress which is established on January 3, 2021?

    Ans: 117th

     

  • Joe Biden is current and 46th U.S. President, What number he stands as Democratic President in the history of U.S.?

    Ans: 16th

  • Donald Trump was________ president of Republican party.

    Ans: 19th

    • View All

Blog Category

Features

  • বিসিএস, ব্যাংক, শিক্ষক নিবন্ধন, পিএসসিসহ সব ধরনের MCQ প্রশ্ন এবং সমাধান,
  • অধ্যায় অনুযায়ী অনুশীলন,
  • ইংরেজি এবং গণিত এর জন্য সহজ কৌশল,
  • অসংখ্য মডেল পরীক্ষা,
  • পরীক্ষার পর্যালোচনা,
  • সাম্প্রতিক বিষয় নিয়মিত আপডেট,
  • প্রতিদিন পাঁচটি করে vocabulary (Meaning, Synonyms, Antonyms, Example সহ )।

Recent Posts

6871

Students

79846

Questions

150

Model Test

Boibd (www.boibd.com) is an online platform for taking preparation of every government and non government job examination.

Here you will get questions with the solutions of BCS, BANK JOBS, TEACHER'S RECRUITMENT EXAMINATION, PSC and many others. It is also a useful medium to take preparation for University admission exam.

Latest Posts

Useful Links

Contact Us

House # 44, Road # 08, Bloack # D, Niketon, Gulshan-1, Dhaka
Bangladesh.
Phone: 01911673131
Email: kabirdepart@gmail.com

© boiBD, 2024 © All Rights Reserved. Privacy Policy | Terms of Use

  • facebook
  • linkedin
  • twitter