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Average

Correct :

Wrong :

  • 1. A player’s average test score on 4 tests is 78. What must be his score on a 5th test for average score on 5 tests to be 80?
  • Let the score in the 5th test be x.
    The sum of the first 4 tests = 78 X 4=312
    Now it implies ,

    312+x/5=80
    Therefore, x=88    
     

  • 2. The average of a and b is 45.  And the average of b and c is 35, then (a - c) = ?
  • 3. The average of a  set of 12 numbers,which  includes 34,is A. If 34  is removed from the set and 36  is included to the set. What is the average of the new set of numbers in terms of A?
  • 4. The average of x and y is 40 and that of y and z is 35. What is the value of x-z?
  • 5. The average daily earnings of a man who makes Tk. 25 each of the first 9 days, Tk. 30 each of the next 10 days and Tk. 40 each of the last 11 days is Tk.
  • 6. The average of 2, 7, 6 and x is 5 and that of 18, 1, 6, x and y is 10. The value of y is
  • 7. ১০টি সংখ্যার যোগফল ৪৬২। প্রথম চারটির গড় ৫২ এবং শেষ ৫টির পড় ৩৮। পঞ্চম সংখ্যাটি কত?
  • 8. A student was asked to find the arithmetic mean of the numbers 3,11,7,9,15,13,8,19,17,17,21, 14 and x. He found the mean to be 12. What should be the number in place of x?
  • 9. If the average of 5 consecutive is 12, what is the sum of least and the greatest of the integers?
  • Keep the average in middle and place two numbers at left and right.

    Five Numbers are 10,11,12,13,14

    Sum of least and greatest integers =(10+14)=24

  • 10. If the average of z and x is 35, and the average of x and y is 25. Then z – y = ?
  • (z + x)/2 = 35

    z + x = 70 .................... (1)

     

    And,

    (x + y)/2 = 25

    x + y = 50 ................. (2)

     

    (1) - (2), we get,

    z - y = 70 -50 = 20

  • 11. The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then: 
  • 12. A worker is paid Tk. d an hour for the first 8 hours she works in a day. For every hour after the first 8 hours, she is paid Tk. c an hour. If she works 12 hours in one day, what is her average hourly wage for that day ?  
  • for first  eight hour she is paid= 8d tk
    for remaining 4 hour she is paid= 4c tk
    so , she is averagely paid = 8d+4c/12= 4(2d+c)/12=(2d+c)/3

  • 13. A researcher computed the mean, the median and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?  
  • If we add or subtract a constant to each term in a set the standard deviation will not change..
    If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.

  • 14. Let A be the set of primes less than 6, and B be the set of positive odd numbers less than 6. How many different sums of the form a + b are possible, if a is in A and b is in B?
  • A= { 2, 3, 5} and
    B= {1, 3, 5}
    . Any of the 3 numbers in A could be added to nay of the 3 numbers in B, so 9 sums could be formed. However, there could be some duplication. List the sums systematically; first add 1 to each number in A, then 3, and then 5: 3, 4, 6; 5, 6(x), 10; 7, 8, 10(x). there are 7 different sums

  • 15. A researcher computed the mean, the median and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
  • If we add or subtract a constant to each term in a set the standard deviation will not change..
    If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.

  • 16. At 3 A.M. the temperature was 13° below zero. By noon, it had risen to 32°. What was the average hourly increase in temperature?
  • Total Difference = 32 - (-13) = 45

    Average hourly increase = 45/9=5

  • 17. The average of 10 numbers is -10. If the sum of 6 of them is 100, what is the ; average of the other 4?
  • let,
    sum of 6 of them=x=100

    The sum of 4 of them=y
    so,x+y/10=-10
    y=100
    so average=-200/4=-50

  • 18. If the average of 2x and 4x is 12, then x is equal to
  • here,
    2x+4x/2 = 12
    or,6x/2=12
    or,x=4

  • 19. The average of three numbers is 24, if two of the numbers are 21 and 23, the third number is ---
  • sum of three number= 24 X 3=72
    sum of two numbers are= 21+23=44
    so third number is = 72-44=28

  • 20. If taka 45000 was invested in a share when the price per share was taka 90 and taka 3000 was invested when the price per share was taka 60, what was the average price per share purchased?
  • at 90 tk price,
    total share he bought= 45000/90=500 share
    at 60 tk price,
    total share he bought= 3000/60=50 share
    total investment=  45000+3000 tk= 48000 tk

    total share= 500+50=550 
    average cost=48000/550=87.27 tk

  • 21. The average daily income of Mr. A and Mr. B is Tk. 350, of Mr. B and Mr. C is Tk. 365, and of Mr. A and Mr. C is Tk. 340. What is the weekly income of Mr. A if he works 5 days in a week?
  • 22. The electric company charges Tk. 0.30 per kilowatt-hour (KWH), Rahim used 2800 KWH in April, 3200 KWH in May, and 3600 KWH in June. What was his average cost of electricity for the 3 months?
  • total used= 2800+3200+3600=9600 kwh
    total cost= 0.30 X 9600=2880 tk
    average= 2880/3=960 tk

     

  • 23. The average of first five prime numbers is---
  • 24. If 1/(x+y) = 4 then X=?
  • 25. If the average of 4, 5, 6 and P is 7, what is the value of P?
  • 26. An analysis of the monthly incentives received by 5 salesmen: The mean and median of the incentives is $7,000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest incentive received by the 5 salesmen in the month?          
  • The arithmetic mean of 5 observations is $7000.
    Therefore, the sum of these 5 observations is 5 * 7000 = $35,000.
    The median is $7000.
    Let us say their incentives in ascending order are a, b, c, d and e.
    So, c = 7000 and a + b + c + d + e = $35,000
    The only mode is $12,000. So, the maximum number of observations among the 5 will be in $12,000.
    The only possibility is that both d and e got an incentive of $12,000 each.
    So, c + d + e = 7000 + 12000 + 12000 = $31,000
    Therefore, a + b = 35,000 - 31,000 = 4000.
    a and b have to be two different values as the only mode is $12,000.
    So, a has to be $1000 and b has to be $3000.
    The difference between the highest and the lowest is therefore 12,000 - 1000 = $11,000

  • 27. The average weight of a group of 30 friends increases by 1 kg when the weight of their football coach was added. If average weight of the group after the weight of the football coach is 31 kgs, what is the weight of their football coach in kgs?          
  • The new average weight of the group after including the football coach = 31
    As the new average is 1kg more than the old average, old average without including the football coach = 30 kgs.
    The total weight of the 30 friends without including the football coach = 30 X 30 = 900.
    After including the football coach, the number people in the group increases to 31 and the average weight of the group increases by 1kg.

    Therefore,
    the total weight of the group after including the weight of the football coach = 31 X 31 = 961 kgs.
    Therefore, the weight of the football coach = 961 - 900 = 61 kgs.

  • 28. A basketball team has won 15 games and lost 9. If these games represent 16(2/3) percent of the games to the played, then how many more games must the term win to average 75 percent for the season?
  • 29. If the total sales for a business in a certain year were Tk. 150000 what were the sales in June, if June sales were half the monthly average?
  • here, 
    yearly sales =150000 tk
    so, monthly sales=150000/12=12500 tk.
    then,the sales in June, if June sales were half the monthly average=12500/2=6250 tk

  • 30. The sum of daily income of P, Q and R is Tk. 90. If Q earns Tk. 10 more than P and R earns double of what Q earns, then what is the average of daily income of P and Q?
  • 31. The average score of students on a certain exam was 85.50. On the same exam Raju scored 90. What was Raju’s percent deviation from the average score?
  • 32. Jenny’s average on 4 exams is 80. Assuming she cannot earn more than 100 on any exam, what is the least she can earn on her 5th exam and still have a chance for an average of 84 after seven exams?
  • 33. On Saturday two of students in a class took a test and their average score was 80. On Tuesday, the other students took the test, and their average score was 90. What was the average for the entire class?
  • 34. The average of a set of 12 numbers, which includes 35, is N. If 35 is removed from the set and 38 is added to the set, then what is the average of the new set of numbers in terms of N?
  • 35. ৬, ৮, ১০ এর গানিতিক গড় ৭, ৯ এবং কোন সংখ্যার গানিতিক গড়ের সমান?
  • ৬, ৮, ১০ এর গানিতিক গড়=২৪/৩=৮
    এখন, মনে করি ,
    সংখ্যাটি "ক"
    প্রশ্নমতে,
    ৭+৯+ক/৩=৮
    বা,১৬+ ক= ২৪
    বা,ক=২৪-১৬=৮
    সুতরাং,ক=৮

  • 36. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
  • Average of 20 numbers = 0.

     Sum of 20 numbers (0 x 20) = 0.

    It is quite possible that 19 of these numbers may be positive and if their sum is X then 20th number is (-X).

  • 37. The present ages of three person in proportions  4 : 7 : 9 Eight years ago, the sum of their ages was 56. Find their present ages (in year).
  • Let their present ages be 4x, 7x and 9x years respectively.

    Then, (4x - 8) + (7x - 8) + (9x - 8) = 56

    => 20x = 80

    => x= 4.

    Therefore, Their present ages are 4x = 16 years,7x = 28 years and 9x = 36 years respectively.

  • 38. The average of 2, 7, 6 and x is 5 and the average of 18, 1 6, x and y is 10. What is the value of y?
  • 39. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
  • Let there be x pupils in the class.

    Total increase in marks =( x × ½) = x/2

    So, x/2 = (83 - 63)

    => x/2 = 20

    => x= 40.

  • 40. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
  • Required average = ((55 x 50) + (60 x 55) + (45 x 60))/(50+60+45)

    =(2750 + 3300 + 2700)/160

    = 8750/160

    = 54.68

  • 41. A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
  • Since the month begins with a Sunday, to there will be five Sundays in the month.

    Required average = ((510 x 5) + (240 x 25))/30

    = 8550/30

    =285

  • 42. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
  • Required average = (50.25 x 16 + 45.15 x 8)/(16+8)

    = (804 + 361.20)/24

    = (1165.20)/24

    = 48.55

  • 43. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
  • Let A, B, C represent their respective weights. Then, we have:

    A + B + C = (45 x 3) = 135 .... (i)

    A + B = (40 x 2) = 80 .... (ii)

    B + C = (43 x 2) = 86 ....(iii)

    Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)

    Subtracting (i) from (iv), we get : B = 31.

    B's weight = 31 kg.

  • 44. In Ashik's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Ashik and he thinks that Ashik's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Ashik?
  • Let Ashik's weight by X kg.

    According to Ashik, 65 < X < 72

    According to Ashik's brother, 60 < X < 70.

    According to Ashik's mother, X <= 68

    The values satisfying all the above conditions are 66, 67 and 68.

    Required average = (66 + 67 + 68)/3

    = 201/3 = 67 kg.

  • 45. A car owner buys petrol at Tk.7.50, Tk. 8 and Tk. 8.50 per litre for three successive years.. What approximately is the average cost per litre of petrol if he spends Tk. 4000 each year?
  • Total quantity of petrol

    consumed in 3 years  =  (4000/7.50 + 4000/8 + 4000/8.50) litres

    = 4000(2/15 + 1/8 + 2/17) litres

    = 76700/51 litres

    Total amount spent = Tk. (3 x 4000) = Tk. 12000.

    Average cost = Tk. (12000 x 51)/76700

    = Tk. 6120/767 = Tk. 7.98

  • 46. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years.. The present age of the husband is:
  • Sum of the present ages of husband, wife and child

    = (27 x 3 + 3 x 3) years = 90 years..

    Sum of the present ages of wife and child

    = (20 x 2 + 5 x 2) years = 50 years..

    Husband's present age = (90 - 50) years = 40 years.

  • 47. The average monthly income of P and Q is Tk. 5050. The average monthly income of Q and R is Tk. 6250 and the average monthly income of P and R is Tk. 5200. The monthly income of P is:
  • Let P, Q and R represent their respective monthly incomes.

    Then, we have:

    P + Q = (5050 x 2) = 10100 .... (i)

    Q + R = (6250 x 2) = 12500 .... (ii)

    P + R = (5200 x 2) = 10400 .... (iii)

    Adding (i), (ii) and (iii), we get:  2(P + Q + R) = 33000 

    or,   P + Q + R = 16500 .... (iv)

    Subtracting (ii) from (iv), we get P = 4000.

    P's monthly income = Tk. 4000.

  • 48. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
  • Let the average age of the whole team by x years..

    => 11x - (26 + 29) = 9(x -1)

    => 11x - 9x = 46

    => 2x = 46

    => x = 23.

    So, average age of the team is 23 years.

  • 49. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
  • Total weight increased = (8 x 2.5) kg = 20 kg.

    Weight of new person = (65 + 20) kg = 85 kg.

  • 50. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
  • Average of 20 numbers = 0.

    Sum of 20 numbers (0 x 20) = 0.

    It is quite possible that 19 of these numbers may be positive

    and if their sum is a then 20th number is (-a).

  • 51. A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?
  • Total sale for 5 months = Tk. (6435 + 6927 + 6855 + 7230 + 6562) = Tk. 34009.

    So, Required sale = Tk. [(6500 x 6) - 34009]

    = Tk. (39000 - 34009)

    = Tk. 4991.

  • 52. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years.. What is the average age of the family?
  • Required average = (67 x 2 + 35 x 2 + 6 x 3)/(2+2+3)

    = (134 + 70 + 18)/7

    = 222/7

    = 31(5/7) years.

  • 53. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
  • Required run rate = (282 - (3.2 x 10))/40

    = 250/40 = 6.25

  • 54. If the average of 7, 13, p and q is the average of (p+11) and (q-9)?
  • Average, (7+13+p+q) /4 = 17

    Or, 20+p+q = 68

    or, p + q =48

    Again, average = (p+11)+(q-9)/2

                                = (p+q+2)/2

                               = (48+2)/2

                               = 25

  • 55. On Tuesday, 30 of the students in a class took a test and their average score was 83.5. On Thursday, the other 5 students took the test, and their average score was 94. What was the average for the entire class?
  • Average = (30×83.5)+(5×94) / (30+5)

                   =85 or, 85%

  • 56. Three math classes X, Y, and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes?
  • Let no of people in class X,Y,Z be x,y,z respectively,
    total x = 83x
    total y = 76y
    total z = 85z

    total(x+y) = 79(x+y)
    total(y+z) = 81(y+z)

    implies
    83x + 76y = 79(x+y) --------1
    76y + 85z = 81(y+z) --------2


    1 is 3y=4x
    2 is 5y=4z

    average of 3 classes = total( x + y + z )/( x + y + z)

    = (83x+76y+85z)/( x + y + z)

    = 978/12

    = 81.5

  • 57. Average cost of 5 apples and 4 mangoes is 36 taka. The average cost of 7 apples and 8 mangoes is 48 taka. Find the total cost of 24 apples and 24 mangoes.
  • (5a+4m)=36*9=324

    (7a+8m)=48*15=720

  • 58. The average temperature on Wednesday, Thursday and Friday was 25°C. The average temperature on Thursday, Friday and Saturday was 24°C. If the temperature on Saturday was 27°C what was the temperature on Wednesday?
  • Thurs + Fri + Sat = 24 * 3 = 72

    Sat = 27

    So, Thurs + Fri = 72 - 27 = 45

    Again,

    Wed + Thurs + Fri = 25 * 3 = 75

    or, Wed = 75 - (Thurs + Fri)

    or Wed = 75 - 45

              = 30

  • 59. When student weighting 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?
  • Let the average weight of the 59 students be A.
    So the total weight of the 59 of them will be 59 * A.

    The questions states that when the weight of this student who left is added, the total weight of the class = 59A + 45
    When this student is also included, the average weight decreases by 0.2 kgs.

    Thus,

    (59A + 45) / 60 = A - 0.2

    => 59A + 45 = 60A - 12
    => 45 + 12 = 60A - 59A
    => A = 57

  • 60. The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?
  • The average of 5 quantities is 6.
    Therefore, the sum of the 5 quantities is 5 * 6 = 30.

    The average of three of these 5 quantities is 8.
    Therefore, the sum of these three quantities = 3 * 8 = 24

    The sum of the remaining two quantities = 30 - 24 = 6.
    Average of these two quantities = 6 / 2 = 3

  • 61. After 3 semesters in college, Jim has a 3.0 GPA. What GPA must Jim attain in his fourth semester if he wishes to raise his GPA to a 3.1?
  • To solve an averages problem, you should multiply for the products of the average.

    In this case, a 3.0 GPA after 3 semesters gives us 9. (3 times 3.)

    We also know that after the fourth semester, the cumulative GPA is supposed to be a 3.1.

    Hence, this multiplier’s product is 12.4. (3.1 times 4.)

    Subtracting 9 from 12.4 gives you GPA  3.4.

  • 62. Average mark in Math in a class of 40 students is 45. Average mark of all the 30 boys is 50. Then the average mark obtained by the girls is:
  • Total marks of 40 students = 45 * 40

                                                     = 1800

    Total marks of 30 boys = 50 * 30

                                              = 1500

    Total marks of 10 girls = 1800 - 1500

                                             = 300

    Average marks of 10 girls = 300/10

    &

  • 63. The electric company charges Tk 0.30 per kilowatt-hour (KWH). Rahim used 2800 KWH in April, 3200 KWH in May, and 3600 KWH in June. What was his average cost of electricity for the 3 months?
  • For April,

    Cost of electric bill = (2800 * 0.30) tk

                                 = 840 tk

    For May,

    Cost of electric bill = (3200 * 0.30) tk

                                 = 960 tk

    For June,

    Cost of electric bill = (3600 * 0.30) tk

                                 = 1080 tk

    Total Cost of 3 Months = (840 + 960 + 1080) tk

                                  &n

  • 64. The average of X and Y is 40, and the average of Y and Z is 35. What is the value of(X-Z)?
  • (X + Y) / 2 = 40

    or, (X + Y) = 80

    Again,

    (Y + Z) / 2 = 35

    or, (Y + Z) = 70

    Now,

    (X + Y) - (Y + Z) = 80 - 70

    or, X - Z = 10

  • 65. The average of 10 numbers is 7. What will be the new average if each of the numbers is multiplied by 8?
  • Each of the 10 number is being multiplied by 8. Thus, multipying the average by 8 will seek out the answer.

    Average 7 * 8 = 56

  • 66. The average of 7 numbers is 12. After discarding one number, the average becomes 11. What is the discarded number?
  • Total of 7 numbers = 12x7 = 84
    Total of 6 numbers = 11x6 = 66

    Discarded number = 18

  • 67. If the average of the four numbers M, 2M+3, 3M-5 and 5M+1 is 63 what is the value of the M?
  • (M + 2M + 3 + 3M - 5 + 5M + 1) / 4 = 63

    or, (11M - 1) = 63 * 4

    or, 11M = 252 + 1

    or, 11M = 253

    or, M = 253 / 11

    or, M = 23

  • 68. The average mark obtained by 15 students was 10 and the average mark obtained by 10 students was 15. What was the average mark obtained by all students?
  • Total mark of first 15 students = 15 * 10 = 150

    Total mark of first 10 students = 15 * 10 = 150

     

    Total mark of 25 students = 150 + 150 = 300

    Average = 300 / 25 = 12

  • 69. Set X contains 10 consecutive integers. If the sum of the 5 smallest members of set X is 265, what is the average of the 5 largest members of Set X?    
  • x+x+x+x+x+1+2+3+4+5 = 265

    or, 5x + 15 = 265

    or, 5x = 265 - 15 = 250

    or, x = 50

    The largest 5 member of the set is,

    50+6 = 56

    50+7 =57

    50+8 = 58

    50+9= 59

    50+10= 60

    Then,

    Average = (56+57+58+59+60) / 5

                  = 290/5

                  = 58

  • 70. The average weight of 39 students is 30kg. By the admission of a new student, the average comes down to 29.8 kg. Find the weight of the new student.    
  • 30*39 = 1170

    29.8*40 = 1192

    Weight of new student = 1192 - 1170

                                    = 22

     

  • 71. On Tuesday, 30 of the students in a class took a test and their average score was 83.5. On Thursday, the other 5 students took the test, and their average score was 94. What was the average for the entire class?
  • 72. The average of five numbers is 25. After one of the numbers is removed, the average of the remaining is 31. What number has been removed?
  • Total of 5 number is: 25*5 = 125

    Total of 4 number is: 31*4 = 124

     

    Thus, the removed number is= 125-124 = 1

  • 73. Because Meena's test turned out to be more difficult than she intended it to be, the teacher decided to adjust the grades by example, if a student missed 25 points, she received a 87.5 instead of 75. Before the grades were adjusted the class average was M. What was the average after the adjustment, if the total mark of the test is 100?
  • Current average = M

    Total Mark is 100

    So the new average is (100+M)/2 = 50+M/2

  • 74. If the average of a and b is 45, and the average of b and c is 35, then  (a-c)=? 
  • here,
    a+b/2=45
    or,a+b=90
    again,
    b+c/2=35
    or,b+c=70
    so,
    a+b-b-c=90-70=20

  • 75. The average of six numbers is 3. 95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers? 
  • sum of six numbers = 6 x 3.95 =23.7

    sum of two of them = 2 x 3.4 = 6.8

    sum of other two = 2 x 3.85 =7.7

     

    So Sum of four numbers = 14.5 

    So the remaining two numbers' sum = 9.2

    Avg of the two = 4.6

     

  • 76. If the average (arithmetic mean) of a, b, and c is 40, what is the average (arithmetic mean) of (3a + 10), (3b +10), and (3c+10)?
  • (a + b + c) / 3 = 40

    or, a + b + c = 120

    or, 3 * (a + b + c) = 120 * 3

    or, 3a + 3b + 3c = 360

    or, 3a + 3b + 3c + 30 = 360 + 30

    or, (3a + 10) + (3b + 10) + (3c + 10) = 390

    or, [(3a + 10) + (3b + 10) + (3c + 10)] / 3 = 390/3

                                                            = 130

  • 77. The average of five numbers is 6.9. If one of the numbers is deleted, the average of the remaining numbers is 4.4. What is the value of me number deleted?
  • Total of 5 number is = 6.9 * 5 = 34.5

    Total of 4 number is = 4.4 * 4 = 17.6

    Thus, the deleted number is = (34.5 - 17.6)

                                            = 16.9

  • 78. At present the total age of Rahim, Karim and Akkas is 81 years. What was their average age three years ago?
  • 3 years ago, their total age was = 81 - (3*3) = 72

    Average of 3 person's age = 72/3

                                          = 24

  • 79. The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
  • Total weight increased = (8 x 2.5) kg = 20 kg.

    Weight of new person = (65 + 20) kg = 85 kg.

  • 80. If the two digit integers M. and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N?
  • M=10x+y
    N=10y+x
    M+N=11x+11y=11(x+y)
    In other words the answer is a multiple of 11.
    Now the question becomes " which of the following is NOT a multiple of 11?"
    answer----->181----->choice A

  • 81. The average of a and b is 40 and the sum of b and c is 70. What is the value of a-c?
  • (a + b)/2 = 40

    or, (a + b) = 80 .............................................. (1)

    and,

    b + c = 70 .................................. (2)

    (1) - (2), we get,

    a + b - b - c = 80 - 70

    or, a - c = 10

  • 82. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the whole team?
  • Let the average age of the whole team by x years.

    11x - (26 + 29) = 9(x -1)

    11x - 9x = 46

    2x = 46

    x = 23.

    So, average age of the team is 23 years

  • 83. The average of 5 positive integers is 60. If the average of 3 of these integers is 67, what is the greatest possible value that one of the other two integers can have?
  • Total of 5 positive integer = 60*5 = 300

    Total of 3 of these integer = 67*3 = 201

     

    Then, The other two number is = (300 - 201) = 99

    Thus, if one of the number has to the greatest, another has to be the least, and the least positive integer is 1.

    So, the greatest possible value = (99 - 1) = 98

  • 84. If the average of 11, 17, x and y is 19, what is the average of (x+5) and (y-7)?
  • (11 + 17 + x + y)/4 = 19

    or, (11 + 17 + x + y) = 19*4 = 76

    or, x + y = 76 - 11 - 17

    or, x + y = 48

     

    Now,

    [(x+5) + (y-7)]/2 = (x+5+y-7)/2 = [(x+y) -2]/2 = (48 -2)/2 = 46/2 = 23

  • 85. In a class the average mark in an exam is 70. The average of students who scored bellow 60 is 50. The average of students who scored 60 or more is 70. If the total number of students in this class is 20, how many students scored less than 60?
  • 86. What is the value of x if the average of 105,117, 125 and x is 115?
  • (105 + 117 + 125 + x)/4 = 115

    347 + x = 460

    x = 460 - 347 = 113

  • 87. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
  • x= age of the youngest child

    x+x+3+x+6+x+9+x+12=50

    x=4

  • 88. Pick the odd one out 331, 482, 551,263,383,242, and 111
  • All1

  • 89. Find the smallest number of oranges that can be distributed completed among 4,6,10 or 18 children.
  • লসাগু=১৮০

  • 90. In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?
  • x+y/2+(y+z)/2+(z+x)/2=2+3+4

    x+y+z=9

    avg=(x+y+z)/3=3

  • 91. The average of 8, 11 and x is 12.what is the value of x? 
  • (8+11+x)/3 = 12

    or, 8+11+x = 36

    or, x = 36 - 8 - 11

    or, x = 17

  • 92. The average of 6 numbers is 8.5.when one number is discarded the average of the remaining numbers becomes 7.2. What is the number?
  • 8.5 * 6 = 51

    7.2 * 5 = 36

    The omitted number is (51 - 36) = 15

  • 93. Reza’s average in four tests is 80%. What marks does he need in his fifth test to raise his average to 84%?
  • (84 X 5) - (80 X 4)

    420-320 = 100 (Ans)

  • 94. If the sum of the 3 consecutive integers is 240, then the sum of the two larger integers is:
  • 95. The average weight of 8 persons increases by 2.5 kg when a new person conies in place of one of them weighing 65 kg. What might be the weight of the new person?
  • 65+(8X2.5) = 65+20= 85 (ans.)

  • 96. The average of 6 numbers is 9, when one number is discarded the average of the remaining numbers becomes 7.2. What is the discarded number?
  • The average of 6 numbers is 9 --> the sum of 6 numbers = (mean)*(number of terms) = 9*6 = 54.

    The average of 5 numbers is 7.2 --> the sum of 5 numbers = (mean)*(number of terms) = 7.2*5 = 36.

    The discarded number = 54 - 36 = 18.

  • 97. The average of 6 numbers is 8.5, when one number is discarded the average of the remaining numbers becomes 7.2.what is the discarded number ?
  • 98. Sum of P and Q is 72 and the value of R is 42. What is the average of P, Q and R?
  • P+Q= 72

    R=42

    Then,

    P+Q+R= 72+42 = 114

    Average of P,Q,R = 114/3 = 38

  • 99. কামাল,জামাল এবং সালাম এর দৈনিক আয় একত্রে ৯০ টাকা । যদি জামাল কামালের চেয়ে ১০ টাকা বেশি আয় করে এবং সালামের আয় জামালের আয়ের দ্বিগুন হয়,তবে কামাল ও জামালের আয়ের গড় কত ?
  • ধরি,
    জামালের আয় = ক টাকা

    কামালের আয় = ক - ১০ টাকা

    সালামের আয় = ২*ক টাকা

    এখন,

    ক + ক - ১০ + ২*ক = ৯০

    বা, ৪*ক = ৯০+ ১০

    বা, ৪*ক = ১০০

    বা, ক = ১০০/৪ = ২৫ টাকা

     

    অতএব,

    জামালের আয় = ২৫ টাকা

    কামালের আয় = ২৫ - ১০ = ১৫ টাকা

    তাদের গড় আয় = (২৫ + ১৫) / ২ = ৪০/২ = ২০ টাকা
     

  • 100. ১০টি সংখ্যার যোগফল ৪৬২ । প্রথম ৪টির গড় ৫২ এবং শেষ ৫টি গড় ৩৮ হয় পঞ্চম সংখ্যাটি কত?
  • ধরে নেই, সংখ্যাটি ক।

    তাহলে,

    ৫২*৪ + ক + ৩৮*৫ = ৪৬২

    বা, ক = ৪৬২ - ২০৮ -  ১৯০

    বা, ক = ৬৪
     

  • 101. The average of 7 consecutive numbers is 20. The largest of these numbers is:
  • Let, the numbers be x, x+1, x+2, x+3, x+4, x+5, x+6

    Sum of 7 consecutive number be= 20X7= 140

    A.T.Q. 

    x, x+1, x+2, x+3, x+4, x+5, x+6= 140

    7x+21 = 140

    7x = 119

    .:. x= 17   .:. The largest number= x+6= 17+6 = 23 (Ans.)
     

  • 102. The average of Selim’s marks in 7 subject is 75. His average in six subjects excluding science is 72. How many marks did he get in Science?
  • 103. If 3a+5b=10 and 5a + 3b=30, what is the average (arithmetic mean) of a and b?
  • 3a+5b=10 ..................... (1)

    5a + 3b=30 ....................... (2)

    We get from (1) + (2),

    8a + 8b = 40

    or, a + b = 5 (Dividing both sides by 8)

    Now, The average would be,

    (a + b)/2 = (5)/2 = 2.5

  • 104. Average of 17 even consecutive integers is 42. What is the third integer from the beginning of the series when the integers are arranged in an increasing sequence?
  • (17+1)./2=9

    So,9th number in the series is 42

    1st number in the series=42-8x2=26

    3rd number in the series=26+2x2=30

  • 105. The average of a series of consecutive odd numbers is 33? If there are 7 numbers in the series, what is the lowest number in the series?
  • Let,numbers are,x,x+2,x+4,x+6,x+8,x+10 and x+12

    (7x+42)/7=33

    x=27

  • 106. 2700 chocolates were distributed among the students of a class. If each student got 3 times as many chocolates as the number of students in the class, find the number of students in the class.
  • 107. The average of four consecutive odd positive integers is always    
  • avg(1, 3, 5, 7 ) = 16/4 = 4

    avg(15,17,19,21) = 72/4 = 18

  • 108. The average of four consecutive odd positive integers is always    
  • 109. Find the average of all whole number 1 and 100 that end in 3?
  • (3 + 13 + 23 + 33 + 43 + 53 + 63  +73 + 83 + 93 )/10

    Sum= n/2(2a +(n-1)d)

      = 10/2  (6 + 9X10) = 480

    Avg = 48

  • 110. Tk. 51 is distributed between Sumi and Meem in such a way that Sumi receives Tk. 3 less than twice the amount received by Meem. The amount (in Tk.) received by Sumi is:     
  • 111. If mamun were twice as old as he is now he would be 40 years older than jamal, if jamal is 10 years younger than mamum how old as mamum ?    
  • 112. If the average of 5,6,7 and w is 8 the value of w is-
  • 5+6+7+w = 8×4

    => 18+w = 32

    => w = 32-18 = 14 (Ans.)

  • 113. If Tk. 4500 was invested in a share when the price per share was tk. 90 and tk. 30000 was invested when price per share was tk. 60, what was the average price per share purchased?  
  • *সঠিক উত্তর নেই

    Total number of share = 4500/90 + 30000/60 = 50+500 = 550

    .:. Average price per share = (4500+30000)/550 = 62.73 (Ans)

  • 114. Rahim is now 10 years youngere than karim. If in 5 years karim becomes twice as old as rahim, how old will rahim be in 3 years ?  
  • Let, Karim is x years old

    So, Rahim = (x-10) years old

    According to question,

    (x+5) = 2(x-10+5)

    => x+5 = 2x-10

    => x=15

    So, After 3 years Rahim will be = x-10+3 = 8 years (Ans.)

  • 115. The average age of 30 students is 10 years and that of another group 5 of them is 14 years. What in the average age of the remaining students?  
  • 116. The average of eight numbers is 14 and the average of six of these numbers is 16. What is the average of the remaining two numbers?  
  • 117. The numbers of students in each section of a school is 24. After admitting new students, three new sections were started . Now, the total number of sections is 16 and there are 21 students in each section. How many new students were admitted?  
  • 118. The sum of Rahim’s age and his son’s age is 55 years. 5 years ago Rahim’s son was 29 years younger than Rahim. What is the  son’s present age?
  • 119. In a class of 22 students, 21 students get an average of 44 marks. If the remaining student get 66 marks, the average marks of the whole class is –    
  • 21 X 44 = 924

    924 + 66 = 990

    990/22 = 45

  • 120. A truck driver must complete a 180 mile trip in 4 hours. If his average speed is 50 miles per hour for first 3 hours, then how fast must he travel for the final hour?
  • 121. The average of a,b,c is 6 and a-b = 4, ab = 21, what is the value of c?
  • 122. what is the average (arithmetic mean) of all multiples of 10 from 10 to 4500 inclusive?  
  • 123. A,B,C started a business with their investment in the ratio 1:3:5 .After 4 month A invested the same amount as before and B, as well as C, withdrew half of their investment.The ratio of their profit at the end of the year is-    
  • Let their initial investments be x, 3x and 5x respectively.
      Then

    X : Y : Z = (x * 4 + 2x * 8) : (3x * 4 + 3x/2 * 8 ): (5x * 4 + 5x/2 * 8 )  = 20x : 24x : 40x= 5 : 6 : 10
     

  • 124. if the mean of 5 observations X, X + 2 ,X + 4, x + 6 and X + 8 is 11 then the mean of the last 3 observations is-  
  • First,

    you need to solve for x:
     (x + x + 2 + x + 4 + x + 6 + x + 8) / 5 = 11
    x + x + 2 + x + 4 + x + 6 + x + 8 = 55
    5x + 20 = 55
    5x = 35
    x = 7
    Now, substitute for x in each of the last three terms:
     x + 4 + x + 6 + x + 8 = (7 + 4) + (7 + 6) + (7 + 8) = (11) + (13) + (15) = 39 / 3 = 13
    The mean is 13.

  • 125. Consider that w+x=-4, x+y=25 and y+w=15. Then the average of w,x,y is -
  • 126. Consider that w+x=-4, x+y=25 and y+w=15. Then the average of w,x,y is-
  • 127. Last year Salem received 26 paychecks. Each of his first 6 paychecks was Tk.750; each of his remaining paychecks was Tk. 30 more than each of his first 6 paychecks. To  the nearest taka, what was the average amount of his paychecks for the year?
  • 128. ১০ থেকে ৬০ পর্যন্ত যে সকল মৌলিক সংখ্যার একক স্থানীয় অঙ্ক ৯ তাদের সমষ্টি কত?
  • 129. প্রথম ৬টি স্বাভাবিক সংখ্যার সমষ্টি কত?
  • 130. পরপর তিন টি ক্রমিক সংখ্যার গুণফল ১২০ হলে তাদের যোগফল কত হবে?
  • 131. The average of 8 number is 14 . The average of six of those numbers is 16 . The average of the remaining two numbers is ---
  • 132. The sum of all even natural numbers between 1 and 31 is:
  • 133. Average of all prime numbers between 30 to 50 is:
  • 134. The average of the three numbers and is 45. X is greater than the average of y and z  by 9. The average of y and z is greater than y by 2. Then the difference of x and z is.  
  • 135. The average age of a group of 15 employees is 24 years, if 3 more employees join the group, the average age increases by 2 years. Find the average age of the new employees.
  • 136. The price of lunch for 15 people was Tk 207.00 including 15% service charges. What was the average price of lunch per person excluding the service charge? 
  • 137. The average age of a group of 15 employees is 24 years. If 5 more employees join the group, the average age increases by 2 years. Find the average age of the new employees.  
  • Sum of the ages of (15+5) = 20 employees => 20×(24+2) = 520 years
    Sum of the ages of 15 employees => 15×24 = 360
    Sum of the ages of new 5 employees = (520-360) = 160
    Average = 160/5 = 32. 

  • 138. A batsman has a certain average of runs for 12 innings. In the 13" inning, he scores 96 runs thereby increasing his average by 5 runs. What is his average after the 13 innings?   
  • Average of 12 innings = x
    According to the question:
    (12x+96)/13 = x+5
    x = 96-65 = 31.
    Average in 13 innings = 31+5 = 36

  • 139. করিমের বার্ষিক আয় রহিমের চেয়ে ১০% বেশী, অন্যদিকে রহিমের বার্ষিক আয় খালেকের  আয়ের চেয়ে ২০% বেশী। খালেকের মাসিক আয় ২০০০ টাকা হলে, ৩ জনের মােট মাসিক আয় কত?
  • 140. The average of 6 numbers is 25. If 3 more numbers, with an average of 22 are added to these numbers, what will be the average of  the combined 9 numbers?
  • Sum of 6 numbers = (6×25) = 150.
    Sum of 3 additional numbers = (3 × 22) = 66.
    Sum of (6 + 3) =9 numbers = (150+66)=216
    .:. average of 9 numbers = 216/9 = 24
  • 141. Consider that w + x = – 4, x + y = 25 and y + w = 15, Then the average of w, x, y is ____
  • w+ x + x + y + y +w = -4 + 25 + 15

    Or, 2w+ 2x + 2y = 36

    Or, 2 (w + x + y) = 36

    Or, w + x + y =18

    Or (w + x + y)/3 = 18/3 = 6

    So, average of w, x, y = 6

  • 142. The average of six numbers is 14. The average of four of these numbers is 15. The average of the remaining two number is -
  • The sum of six numbers  =(14×6=84
    The sum of 4 numbers  =(15×4)=60
    .'. Average remaining two numbers  =84-602=242=12
  • 143. The average of the first and the second of three numbers is 15 more than the average of the second and the third of these numbers. What is the difference between the first and the third of these three numbers?
  • 144. 30 pens and 75 pencils altogether were purchased for Tk.510. If the average price of a pencil was Tk 2, what was the average price of a pen?
  • 145. The average of 6 numbers is 25. If 3 more numbers, with an average of 22 are added to these numbers, what will be the average of the combined 9 numbers?
  • Sum of 6 numbers = (6×25) = 150.

    Sum of 3 additional numbers = (3 × 22) = 66.

    Sum of (6 + 3) =9 numbers = (150+66)=216

    .:. average of 9 numbers = 216/9 = 24

  • 146. In June a baseball team that played 60 games had won 30% of its games played. After a phenomenal winning streak this team raised its average to 50% How many games must the team have won in a row to attain this average?
  • Let, Additional match = x

    Now,

    30% of 60+ x = 50% of (60+x)

    Or, 18+x = 30+0.5x

    Or, x = 24


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