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Here,

Y:Z = 1.5

or, Y/Z = 1.5

or, Y/2=1.5 [Z=2]

So, Y=1.5×2=3

Now, X:Y = 1.5

Or, X/Y = 3/2 [3/2=1.5]

Or, X/3=3/2 [Y=3]

Or, X=9/2=4.5

Here,

Sum of ratios are = ( 1+2+3+4+5)=15

Highest value = (5/15) × 7500 = 2500

Lowest value =(1/15) × 7500= 500

So, the difference =2500-500=2000

Here,  2 hours =2$$\begin{gathered} \times 60 \\ =120 minutes \\ In 3 minutes fill the \\ \tan k 4 litres \\ " 1 " " " "\frac{4}{3}" \\ .\text{'}. " 120 " " " \frac{4\times 120}{3} \\ =160 litre \\ In 2000 litre fill into 160 litre \\ .\text{'}. " 1 " " " \frac{160}{2000} " \\ .\text{'}. " 100 " " " \frac{160\times 100}{2000}" \\ =8 litre \\ .\text{'}. After 2 hours \tan k will be fill 8\% \end{gathered}$$
 

অনুপাতের যোগফল=৩+৭+১০=২০

সুতরাং বাঁশের টুকরোগুলোর সাইজ,

১ম টুকরো=(৬০×৩)/২০=৯ মিটার।

২য় টুকরো=(৬০×৭)/২০=২১ মিটার। এবং

৩য় টুকরো=(৬০×৩)/২০=৩০ মিটার।

Suppose,

number of people =10

total expenditure= G

per person pay= g/10

if n number of people are added then per person pays=G/10+n

So, expenditure reduces= G/10-G/10+n=Gn/100+10n
 

x=2Y/5
Y= 5Z/7

or, Z=7Y/5

So, (Z:X)=(7Y/5) : (2Y/5)

            =(7:2) (Ans.)
 

3*4 + 4*4 = 12 + 16 = 28

The ratio of the number if boys and girls in a school is 3:2
<pre>
To change a ratio to two fractions, put each number, 3 and 2, over the sum of
the two numbers 3+2, or 5. So the two fractions are {{{3/5}}} and {{{2/5}}}.

That means {{{3/5}}}ths of the students are boys and {{{2/5}}}ths of the students are
girls.

Change those to percents:

{{{3/5=60/100="60%"}}}, {{{2/5=40/100="40%"}}}

So 60% of the students are boys and 40% of the students are girls.
</pre>
20% of the boys and 25% of the girls are scholarship holders
<pre>
That means 20% of 60% are boy scholarship holders and 25% of 40% are girl scholarship holders.

Therefore:

20% of 60% = (0.20)(0.60) = 0.12 = 12% of the students are boy scholarship
holders, 

and

25% of 40% = (0.25)(0.40) = 0.10 = 10% of the students are girl scholarship
holders. 

That me

12 gallon tub,with 3 gallons of water in the tub: needs {{{9Gal}}} to fill
water in at 3 gal/min, and out at a rate of 1.5 gal/min: Net in at {{{1.5gal/min}}}
 {{{9gal/1.5 (gal/min)}}} = 6 min

3x + 4x =35

x=5

X:Y:Z = 2:3/2:1 = 4:3:2

now, lowest salary is earned by Z, as we can see from the ratio.

Z's salary = 2*90000/9 = 20000 tk

ধরি, ৪র্থ রাশি= x

৩৯২/২৮ = ৭২২/x

বা, ৩৯২x = ৭২২×২৮

সুতরাং, x = ৫১.৫৭

ক্রয়মুল্য ১০০ টাকা হলে ৫০% লাভে বিক্রয়মুল্য (১০০+৫০)=১৫০ টাকা এই বিক্রয়মুল্যের উপর আবার ১০% কমিশন বিক্রয়মুল্য হবে ৯০*১৫০/১০০=১৩৫ টাকা

সুতরাং, মোটের উপর শতকরা লাভ হবে (১৩৫-১০০)=৩৫ টাকা   

মনে করি, দশ বছর পূর্বে পিতার বয়স ছিল ৭x এবং ২x বছর

সুতরাং, বর্তমানে পিতার বয়স হবে ৭x + ১০ বছর

           পুত্রের   ”    ” ২x+ ১০ বছর

প্রশ্নমতে, ৭x +১০ +২x + ১০=৭৪

বা, ৯x + ২০ =৭৪ বা, ৯x=৫৪ =x=৬

সুতরাং, পিতার বর্তমান বয়স ৭*৬+১০=৫২ বছর

     পুত্রের    ”     ”  ২*৬+১০=২২ বছর

সুতরাং, ১০ বছর পর পিতার বয়স ও পুত্রের বয়সের অনুপাত হবে ৫২ + ১০:২২ +১০= ৬২:৩২ = ৩১:১৬

Let the number be x.Then,

3/5x²= 126.15.

x²=(126.15 X 53)= 210.25.

x=√210.25 = 14.5 

let the numbers be 3x, 4x and 7x.
Then, 3x x 4x x 7x = 84x3 = 18144. Therefore, x

Let P age and Q age is 6x years and 7x years.
Then 7x - 6x = 4 <=> x = 4

So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8

80 percent is male and 20 percent is female

ratio= 3:7
sum of ratio=3+7=10
boys are=3/10 X150 =45 

ratio =35:63=5:9

here,
water +container= 18.5
.25water+container=6.5 kg
so,
.75 water =12 kg
so , full weight of water =12/.75=16 kg
so, empty container= 18.5-16.00=2.5 meter

Assume; g = number of girls, b = number of boys
Total number of students = b + g
g / 4 = (b + g) /6
6g = 4(b + g) = 4b + 4g
2g = 4b
2/4 = b/g
b/g = 1/2

Asif got 15x chocholate
Siyam got 7x chocholate
difference=15x-7x=8x
here,
8x=16
so,x=2
so,siyam get 7X2=14 chocolate

here,
one number 3x 
another number 5x
here,
5x+3x=640
or,8x=640
or,x=640/8=80
so ,greater number is = 80 X 5= 400

Go from the choices
Choice (3) 30 and 20 are in the ratio of 6: 4
Five years ago their ages would be 25 and 15 which are in the ratio 5 : 3.
Hence choice (3) is the right answer.

Given two equal glasses are respectively one third =1/3
and one fourth full of milk=1/4
total milk in both glass=1/3+1/4=7/12
water in 1st glass=1-1/3=2/3
water in 2nd glass=1-1/4=3/4
total water=2/3+3/4=17/12
then ratio of milk and water =(7/12)/(17/12)
=>ratio of milk and water =7:17


 

Total capacity of 16 one size container is x 
capacity of one container is x/16 
Total capacity of 8 other size container is x 
capacity of one other size container is x/8 

৬০ লিটার কেরোসিন ও পেট্রোলের মিশ্রনের অনুপাত ৭:৩

কেরোসিন  আছে = ৭/১০ * ৬০ লিটার = ৪২ লিটার

পেট্রোল  আছে ১৮ লিটার

 ঐ মিশ্রনে আর কত লিটার ্পেট্রল মিশালে অনুপাত ৩:৭ হবে।

কেরোসিন এর পরিমাণ অপরিবর্তিত থাকবে, অর্থাৎ ৪২ থাকবে। 

পেট্রল 'ক' গ্রাম যুক্ত করলে অকটেনের পরিমাণ হবে ১৮+ক গ্রাম 

এদের অনুপাত ৪২/(১৮+ক)

প্রশ্নমতে,

৪২/[১৮+ক] = ৩/৭

=> ৫৪ + ৩ক = ২৯৪

=> ৩ক = ২৪০

=> ক = ৮০ 

Let he mixes the tea in ratio x : y 
Therefore the cost price = 60x + 65y
and the selling price = 68.20(x + y)

Profit = SP - CP
So 10/100 (60x + 65y) = 68.20(x + y) - (60x + 65y)
or 6x + 6.5y = 8.20x + 3.20y
2.2x = 3.3y
 x/y = 3:2 

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.

Then, sum of their values

= Tk. {(25x/100) + (10 x 2x)/100 + (5 x 3x)/100}

= Tk. (60x/100)

So, 60x/100 = 30

=> x = (30 x 100)/60 = 50.

Hence, the number of 5 p coins = (3 x 50) = 150.

Let the numbers be 3x and 5x.

Then, (3x – 9) / ( 5x – 9) = 12/23

=> 23(3x - 9) = 12(5x - 9)

=> 9x = 99

=> x = 11.

So, The smaller number = (3 x 11) = 33.

Let the fourth proportional to 5, 8, 15 be x.

Then, 5 : 8 : 15 : x

=> 5x = (8 x 15)

So, x = (8 x 15)/5 = 24.

Let 40% of A = (2/3) B

Then, 40A/100 = 2B/3

=> 2A/5 = 2B/3

=> A/B = (2/3) x (5/2) = 5/3

So, A : B = 5 : 3.

Let A = 2k, B = 3k and C = 5k.

A's new salary = 115/100 of 2k = (115/100) x 2k = 23k/10

B's new salary = 110 of 3k = (110/100 x 3k = 33k/10

C's new salary = 120/100 of 5k = (120/100) x 5k = 6k

So, New ratio (23k/10 : 33k/10 : 6k) = 23 : 33 : 60

Given ratio = 1/2 : 2/3 :3/4 = 6 : 8 : 9.

So, 1^st part = Tk. (782 x (6/23)) = Tk. 204

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8

= 5 x (3/5) : (8 x 3/5) = 3:24/5

=> A : B : C = 2 : 3 : 24/5 = 10 : 15 : 24

=> B = (98 x 15/49) = 30.

(x x 5) = (0.75 x 8)   

=> x = (6/5) = 1.20

Let the original salaries of Ravi and Sumit be Tk. 2x and Tk. 3x respectively.

Then, (2x + 4000)/(3x + 4000) = 40/57

=> 57(2x + 4000) = 40(3x + 4000)

=> 6x = 68,000

=> 3x = 34,000

Sumit's present salary = (3x + 4000)

= Tk.(34000 + 4000) = Tk. 38,000.

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

=> ((120/100)x7x) and ((110/100) x 8x)

=> 42x/5 and 44x/5

So, The required ratio = 42x/5 : 44x = 21 : 22.

Quantity of milk = ((60 x (2/3)) litres = 40 litres.

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

Then, milk : water = 40/(20+x)

Now, 40/(20+x) = ½

=> 20 + x =80

=> x = 60.

So, Quantity of water to be added = 60 litres.

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

=> (140/100 x 5x) , (150/100 x 7x) and (175/100 x 8x)       

=> 7x, 21x/2 and 14x.

So, The required ratio = 7x : 21x/2 : 14x

=> 14x : 21x : 28x

=> 2 : 3 : 4.

Let the shares of A, B, C and D be Tk. 5x, Tk. 2x, Tk. 4x and Tk. 3x respectively.

Then, 4x - 3x = 1000

=> x = 1000.

So, B's share = Tk. 2x

= Tk. (2 x 1000) = Tk. 2000.

Let the third number be x.

Then, first number = 120% of x

= 120x/100 = 6x/5

Second number = 150% of x

= 150x/100 = 3x/2

So, Ratio of first two numbers = (6x/5 : 3x)

= 12x : 15x = 4 : 5.

(4/15)A = (2/5)B

=> A = (2/5) x (15/4)B

=> A = (3/2)B

=> A/B = 3/2

=> A : B = 3 : 2.

So, B's share = Tk. (1210 x 2/5) = Tk. 484.

Go from the choices

Choice (3) 30 and 20 are in the ratio of 6: 4

Five years ago their ages would be 25 and 15 which are in the ratio 5 : 3.

Hence choice (3) is the right answer.

x*x : y*y = 2 : 1

x : y = square root (2) : 1

35% * X = 25% * Y

or, 35X = 25Y

or, X /Y = 25 / 35

      = 5 / 7

or, X : Y = 5 : 7

The quantity of milk in the mixture is

7/(7+2) X 729

= 7/9 X 729

= 567mL

The quantity of water then shall be

729 - 567 = 162mL

If the final mixture would contain half milk and half water, there must be equal quantity of both.

So in order to make up for water, we'll need to add

567mL - 162mL= 405mL of water

Required Number is = [420 * 4/ (3+4)] = 240

The first number is= 180/4 =45

The seond number is= 180/3 = 60

Given two equal glasses are respectively one third =1/3

and one fourth full of milk=1/4

total milk in both glass=1/3+1/4=7/12

water in 1st glass=1-1/3=2/3

water in 2nd glass=1-1/4=3/4

total water=2/3+3/4=17/12

then ratio of milk and water =(7/12)/(17/12)

ratio of milk and water =7:17

let's say that there is 1 person over twenty-one.

If there are 3 times as many people aged twenty-one or under as there are people over twenty-one, then there must be 3 people aged twenty-one or under.

This means the TOTAL population = 1 + 3 = 4

The ratio of those twenty-one or under to the total population = 3 : 4

US : Indian = 5 : 2 = 25 : 10 [Multiplying with 5]

Indian : British = 5 : 1 = 10 : 2 [Multiply with 2]

Thus,

US : Indian : British = 25 : 10 : 2

or, US : British = 25 : 2

Profit- 19100

Badrul receive= 9600

Alim receive= 19100-9600 = 9500

Alims total investment= (10000 X 4)+(8000X5)+(5000 X 3)= 95000

9500 tk profit if investment 95000 tk

9600 tk profit if investment 96000 tk

Badruls investment = 96000/12=8000 tk

suppose,
sale=x
gross profit=y
net profit=z
here,
x:y=4:3=(4 x 3) : (3X3)=12:9
y:z=3:1=(3x3) : (3 x1)=9:3
x:y:z= 12:9:3
so,
z:x=3:12=1:4

 

amount of canberry juice=(750 X 20/100)=150 ml
amount of raspberry juice=  (750 X 20/100)=150 ml
amount of apple juice=(750-150-150)=450 ml
so,water:apple juice =250:450=5:9

Let the initial investments of A and B be 3x and 5x.

A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.

B + G = 24

B/G = 1/2

2B = G

Now,

B + 2B = 24

or, 3B = 24

or, B = 8

Then,

8 + G = 24

or, G = 24 - 8

or, G = 16

To make 1:1,

The amount of boys must be equal to Girls.

Thus, additional (16 - 8) or 8 boys is required.

Given that A:P:G=6x:5x:2x and 6x+5x+2x=13x=39, from which it follows that x=3.

Therefore, A-G=6x-2x=4x=12.

Let their present ages be 4x, 7x and 9x years respectively.

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

20x = 80

x = 4.

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

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

140

x 5x

,

114. The ratio of income of Kamran and Dolon is 3:4. The ratio of their expenditures is 4 : 5. Find the ratio of their savings if the savings of Kamran is one fourth of his income? a) 5:4 b) 19:12 c) 4:6 d) 12:19 e) Cannot be determined 115. A sum of Tk. 53 is divided among A,B,C is such a way that A gets Tk. 7 more than what B gets and B gets Tk. 8 more than what C gets. The ratio of their share is: a) 16:9:18 b) 25:18:10 c) 18:25:10 d) 15:8:30 let, C get=x B get=x+8 A get=x+8+7=x+15 according to question, x+x+8+x+15=53 3x=30 x=10 so,C get=10 B get=18 A get=25 so ratio is=25:18:10 116. Two different schools, A and B, have the same number of students. The ration of boys in school A and the boys in school B is 2:1 and the ratio of girls in school A and the girls in school B is 4:5. What is the ratio of the boys in school A to the girls in school A? a) 1:2 b) 2:3 c) 3:4 d) 4:5 e) None of these 117. The ratio of two numbers is 9:15.If the former number is 36 then the next number is: a) 45 b) 60 c) 35 d) 50 e) 30 9X : 15X Now, 9X = 36 or, X = 36/9 = 4 Then, 15X = 15*4 = 60 118. A certain amount was divided between Kashem and Rashed in the ratio of 4:3. If Rashed’s share was Taka 2400, the total amount was: a) 5,600 b) 3,200 c) 9,600 d) 12,000 e) 13,000 Kashem : Rashed = 4 : 3 = 4X : 3X Now, 3X = 2400 or, X = 2400/3 = 800 Now, 4X = 4*800 = 3200 So, total amount was = 2400 + 3200 = 5600 taka 119. If a and b are integers greater than 100 such that a + b = 300, which of the following could be the exact ratio of a to b? a) 9tol b) 5to2 c) 5to3 d) 4 to 1 e) 3 to 2  120. In a sugar-water solution, the ratio of water to sugar is 8:3. If you add 2 kgs of sugar, the ratio becomes 2:1. What was the amount of sugar in the original solution?  a) 4.5 b) 5 c) 8 d) 6 e) none of these Let sugar be x and water be y, Then, y:x = 8:3 or, y/x = 8/3 or, 3y = 8x or, y = 8x/3 ............................. (1) Again, y:(x+2) = 2:1 or, y/(x+2) = 2/1 or, y = 2x + 4 Now, 8x/3 = 2x + 4 or, 8x = 6x + 12 or, 8x - 6x = 12 or, 2x = 12 or, x = 6 Thus, originaly, there were 6 kg of sugar. 121. If A is 4/6 of B and B is 6/8 of C, what is the ratio of C:A ? a) 1:1 b) 4:3 c) 2:1 d) 1:2 e) none of these A = (4/6) * B and, B = (6/8) * C Now, A = (4/6) * (6/8) * C or, A = (4*6/6*8) * C or, A = (4/8) * C or, A = (1/2) * C or, A/C = 1/2 or, C/A = 2/1 122. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is : a) 02:05 b) 03:05 c) 4:5 d) 06:07 e) none of them the third number =x 1st number = 1.2x 2nd number = 1.5x Ratio = 1.2x : 1.5x =4:5 123. Let x : y = 3:4 and x : z = 6 ; 5, then z : y = is? a) 5:3 b) 6:7 c) 4:2 d) 5:8 x:y = 3:4 x:z = 6:5 or 3:5/2 Now, In the common ground of x, z:y = 5/2:4       = 5:4*2       = 5:8 124. The ratio Of 1/5 to 2/7 - is a) 3:5 b) 5:7 c) 7:9 d) 7:10 1/5:2/7 = 1*7:2*5 = 7:10 125. একটি ত্রিভুজের তিনটি বাহুর মাপের অনুপাত ৫:৬:৭ । এর পরিসীমা ১৯৮ সেন্টিমিটার হলে দীর্ঘতম বাহুটি কত সেন্টিমিটার? a) ৪৪ সে.মি. b) ৫৫ সে.মি. c) ৬৬ সে.মি. d) ৭৭ সে.মি. তিনটি বাহুর মাপের অনুপাত ৫:৬:৭ ধরি, বাহুত্রয় ৫ক, ৬ক, ৭ক। তাহলে, ৫ক + ৬ক + ৭ক = ১৯৮ বা, ১৮ক = ১৯৮ বা, ক = ১১ এখন, দীর্ঘতম বাহুটি = ৭*১১ = ৭৭ সেন্টিমিটার 126. If x:y=5:3, then (8x-5y):(8x+5y)=? a) 3:12 b) 8:13 c) 3:11 d) 5:11 e) 5:13 let x=5 and y=3 Then, (8x-5y):(8x+5y) = (8*5-5*3):(8*5+5*3) = (40-15):(40+15) = 25:55 = 5:11 127. Three angles of a triangle are in proportion 5:6:7. Then what is the difference in degrees between the biggest and the smallest angles? a) 15 b) 20 c) 25 d) 30 e) 10 5x+6x+7x=1800 x=100 7x100-5x100=200 128. 35% of Tahia’s income is equal to 25% of Noria's income. The ratio of Tahia’s income to Noria’s income is: a) 7:5 b) 4:3 c) 4:7 d) 5:7 e) 3:4 Let, Tahia's income=x and Noria's income=y  According to ques, 35% of x=25% of y 35x/100=25y/100 x:y=5:7   129. If A/2=B/3=C/4 then A:B:C=? a) 2:3:4 b) 3:4:5 c) 4:3:2 d) 6:4:3 130. A man’s expenditure on food is 3/5 of his expenditure on clothes, find the ratio between his expenditure on food and cloth. a) 2:5 b) 3:5 c) 2:3 d) 5:3 131. কোন ব্যবসায় ক,খ,গ এর মূলধন যথাক্রমে ৩২০,৪০০ এবং ৪৮০ টাকা । তাদের মূলধনের অনুপাত কত ? a) ৩:৪:৫ b) ৪:৫:৬ c) ৬:৮:১২ d) ৬:৯:১৫ e) কোনটি নয় কোন ব্যবসায় ক,খ,গ এর মূলধন যথাক্রমে ৩২০,৪০০ এবং ৪৮০ টাকা  ক,খ,গ এর মূলধন এর অনুপাত = ৩২০ঃ৪০০ঃ ৪৮০                                          =৪ঃ৫ঃ৬ [৮০ দিয়ে ভাগ করুন]   132. পিতা ও পুত্রের বয়সের অনুপাত ৭:৩ । চার বছর পূর্বে তাদের বয়সের অনুপাত ছিল ১৩:৫।বতমানে পুত্রের বয়স কত ? a) ২৪ বছর b) ১৬ বছর c) ১২ বছর d) ৮ বছর e) কোনটি নয় পিতা ও পুত্রের বয়সের অনুপাত ৭:৩ । পিতার বয়স ৭ক পুত্রের বয়স ৩ক  চার বছর পূর্বে তাদের বয়স ছিল ৭ক-৪ এবং ৩ক-৪ অনুপাত ছিল ১৩:৫। অর্থাৎ,  (৭ক-৪)/(৩ক-৪) = ১৩/৫ => ৩৯ক -৫২ = ৩৫ক -২০  => ৪ক = ৩২ => ক =৮ পুত্রের বয়স = ৩ক = ২৪ 133. In a sugar-water solution, the ratio of water to sugar is 8:3. If you add 2 kgs of sugar, the ratio becomes 2:1. What was the amount of sugar in the original solution? a) 4.5 b) 5 c) 8 d) 6 e) None of them the ratio of water to sugar is 8:3. Water is 8x kg Sugar is 3x kg According to the statement of If you add 2 kgs of sugar, the ratio becomes 2:1, 8x : (3x+2) = 2: 1 => 8x/(3x+2) = 2/1 => 8x = 6x + 4 => 2x = 4 => x = 2 So sugar in original solution = 3x = 6kg 134. If a: b is 4:7 and b:c is 5:6, then a:b:c is –     a) 4: 7: 6 b) 14:17:16 c) 20:35:16 d) 20:35:3 e) 4:5:6     a:b = 4:7 = 20:35 b:c = 5:6 = 35:42 So, a:b:c = 20:35:42 (Ans.)     135. If 30% of A= 0.25 of B=1/5th of C, The ratio of A, B and C is-     a) 3:6:5 b) 6:5:4 c) 4:5:6 d) 3:5:6 e) 5:4:6     Correct Ans: 10:12:15     136. One half of a pole is deep into the soil under water, one-third of it is above water level. The total length of the pole in meters is:   a) 8 b) 10 c) 12 d) 16 137. The ratio of ages of a father and his son was 5:1.what is the age of the son father five years,if the ratio of their ages is 3:1 by this time : a) 7 b) 10 c) 12 d) 14 e) 16 138. A and B are in the ratio of 5:4,B and in the ratio of 3:2.what is the ratio of A:C? a) 15:17 b) 16:17 c) 17:18 d) none of these A:B=5:4 =15:12 B:C=3:2 = 12: 8 A:C = 15:8   139. Mr. A and Mr. B have a combined weekly salary of Taka 1,000. If salary of A is increased by 2.5 times and salary of B is increased by 1.5 times, the combined salary would be Taka 1600. What was the original salary of B? a) Taka 100 b) Taka 250 c) Taka 900 d) Taka 1350 140. The business partners Rahim. Sohel and Karim agree to divide their Total profit for a certain year in the ratio 2:5:8. If Sohel’s profit was Taka 20,000 what was the total profit of the business for the year? a) Taka 800 b) Taka 32,000 c) Taka 52,000 d) Taka 60,000 141. in what ratio must a grocer mix two varieties of tea worth Tk 60 per kg and Tk 65 per kg so that y selling the mixture at Tk. 68.20 per kg he may gain 10%?   a) 4:5 b) 3:5 c) 3:4 d) 3:2 e) none 142. a container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume?   a) 8/3 b) 7/3 c) 5/3 d) 4/3 e) none Currently its is 4 units of Alcohol and 4 units of water to make the ratio 3/5 ; how much water has to be added? 4/4+x =3/5 20 = 12+3x x= 8/3 143. Gold is 19 times as heavy as water and copper is 9 times as heavy as water in what ratio should this be mixed to get an alloy r 15 times as heavy as water :   a) 1:4   b) 2:3 c) 1:3 d) 3:2 Let,  the mass of 1 volume unit of water be 1. Then 1 volume unit of gold has mass 19, and 1 volume unit of copper has mass 9.  Now let g be the volume of gold used, and let c be the volume of copper. The total mass divided by the total volume is the density.  (19g + 9c)/(g + c) = 15  19g + 9c = 15g + 15c  4g = 6c  2g = 3c  g/c = 3/2  The volume ratio is 3:2.    144. In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Tk. 1,57,300 was their profit, how much amount did B receive?   a) Tk. 48,400 b) Tk. 36,300 c) Tk. 24,200 d) Tk. 72,600 Here, A:B = 3:2 = 6:4  A:C = 2:1 = 6:3  A:B:C = 6:4:3 B's Share = (B's ratio/Sum of ratio's) X total profit  B share = (4/13)*157300 = 48400 Taka  145. The least whole number which when subtracted from both the terms of the ratio 6:7 gives a ratio less then 16:21 is :   a) 6 b) 4 c) 3 d) 2 Let the whole number is X. Now, according to question, (6 -X) /(7 -X) < 16/21. 21 *(6 -X) < 16 *(7 -X)   126 - 21X < 112 - 16X 126 - 112 < - 16X + 21X 14 < 5X 5X  > 14 X > 2.8 So, Least such whole number would be 3. 146. একটি পাত্রে দুধ ও পানির অনুপাত ৫:১। দুধের পরিমাণ যদি পানি অপেক্ষা ৪ লিটার বেশি হয় তবে পানির পরিমান কত? a) ২ লিটার b) ৪লিটার c) ৬ লিটার d) ১০ লিটার 147. Rahim is 40 years old and Karim is 60 years old. How many years ago was the ratio of their ages 3 : 5? a) 5 years b) 10  years c) 20  years d) 37 years 148. P and Q start a business with initial corresponding profits are in the 13:8. Their corresponding proffits are in  the ratio of 7:5.   If P invested his money for 7 months, find the time period for invested   his money. a) 8 months b) 9 months c) 10 months d) 11 months 149. The ratio of income of a to that of B is 7:5 and the expenditure of A to that of B is 3:2. If   , at the end of the year , each saves tk.500, find the income of A. a) tk.2500 b) tk.3000 c) tk.3200 d) tk.3500 150. A , B and C enter into partnership  by making investments in the ratio 3:5:7 . after a year , C invests another tk.337600 while a withdraws tk. 45600, the ratio of investments then changes to 24:59:87 . How much does  a invest initially ? a) tk.140600 b) tk.141600 c) tk.131600 d) tk.140500 151. ৩ জন জেলে মিলে ৮৮০ টি মাছ ধরেছে। তাদের অংশের অনুপাত ২ : ৪  : ৫ হলে কে কত মাছ পেল? a) ১২০, ২৪০, ৩০০ b) ৬০, ২৪০, ৩৬০ c) ১২০, ১৮০, ৩৬০ d) ১৬০, ৩২০, ৪০০ 152. যদি কিউব-ক এর সাইড ও কিউব-খ এর সাইডের অনুপাত ২ : ১, তা হলে এর তল দুটির অনুপাত কত? a) ১ : ২ b) ২ : ১ c) ৪ : ১ d) ৩ : ১ 153. Find the ratio of purchase price to sell price if there is loss of 12.5% ? a) 7:8 b) 8:7 c) 2:25 d) 25:2 154. If A:B = 3:4, C:B= 5:4, C:D=10:9 then A:B:C:D is - a) 8:6:9:10 b) 8:6:10:9 c) 6:8:10:9 d) 6:8:9:10 155. If x:y=5:3 , then 8x-5y:8x+5y= ? a) 5:11 b) 6:5 c) 5:6 d) 3:8 156. If x : y = 5 : 3, then 8x - 5y : 8x + 5y =? a) 5 : 11 b) 6 : 5 c) 5 : 6 d) 3 : 8 157. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of the dog is equal to 4 leaps of the hare. Compare their speeds : a) 19 : 18 b) 20 : 19 c) 16 : 15 d) 18 : 17 158. In a mixture of 50 liters, milk and water are in the ratio of 3 : 2. How much water should be added to the mixture to make the ratio of the two equal? a) 8 liters b) 10 liters c) 12 liters d) 14 liters 159. Sazu is younger than Rabi by 4 years. If their age ratios are of 7 : 9 respectively, how pld is Sazu? a) 12 Years b) 14 Years c) 14.5 Years d) 41 Years 160. The ratio of the cost price and the selling prices is 4:5. The profit percent is : a) 10% b) 20% c) 25% d) 30% 161. The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250. The sum of the numbers is a) 30 b) 50 c) 60 d) 90 162. একটি কুকুর একটি খরগােশকে ধরার জন্য তাড়া করে। কুকুর যে সময়ে ৪ লাফ দেয়, খরগােশ সে সময়ে ৫ লাফ দেয়। কিন্তু খরগোশ ৪ লাফে যতদূর যায় কুকুর ৩ লাফে ততদূর যায়। কুকুর ও খরগােশের গতিবেগের অনুপাত কত?  a) ১৩ : ১৪ b) ১৬ : ১৫ c) ১৪ :  ১৩ d) ১১ : ১০ 163. The ratio of two numbers is 7: 4. If 8 is added to both the numbers ratio becomes 13:8, what is the smaller number? a) 40 b) 56 c) 38 d) 52 164. There are 2 numbers in the ratio of 4:5 if 4 are subtracted from both numbers the ratio becomes 3:4. What will be the ratio if 4 is added in the both numbers a) 1:2 b) 2:3 c) 5:6 d) 1:4 165. The ratio of boys to girls in a class is 2/3. If 2 boys leave and 4 girls join the class, the ratio of boys to girls become 3/2. How many girls were there in the class originally?  a) 16 b) 20 c) 24 d) None of these 166. The ratio of two numbers is 3:4 and their sum is 630.  The smaller one of the two numbers is - a) 360 b) 270 c) 180 d) 450 two numbers are 3x and 4x 3x + 4x = 630 => 7x = 630 => x = 90 3x = 270   167. A sum of Tk. 53 is divided among A, B, C in such a way that A gets Tk. 7 more than what B gets and B gets Tk. 8 more than C gets. The ratio of their share is-  a) 15:9:18 b) 18:25:10 c) 25:18:10 d) 15:8:30   Let, C gets x tk B gets x + 8 tk A gets x + 8 + 7 tk Total A + B+ C x + 15 + x + 8 + x = 3x + 23 Or, 3x + 23 = tk 53 (given) Or, 3x = 30 Or, x = 10 Ratio of their shares, A : B : C = (x + 15) : (x + 8) : (x) = 25 : 18 : 10 168. এক ব্যবসায়ী ৮০ টাকায় একটি পণ্য বিক্রি করে ২৫% লাভ করে। ব্যয় ও বিক্রি মূল্যের অনুপাত কত? a) ৩:৪ b) ৪:৫ c) ৫:৬ d) ২:৩ 169. A jar contains white, red and green marbles in the ratios 2: 3: 5. six more green marbles are added to the jars, and then the ratio becomes 2 : 3 : 7. How many white marbles are three in the jar? a) 5 b) 6 c) 9 d) 10 Ratio of W : R : G= 2: 3:5। If 6 Green is added, Ratio becomes W: R:G = 2: 3:7 Difference of ratio for 6 marbles = 7 – 5 = 2 For 1 ratio = 3 marbles White marbles = 2×3 = 6 170. The present age of Habib and Shikha are in the ratio of 6 : 4. Five years ago their ages were in the ratio of 5: 3, How old is Habib now? a) 24 b) 30 c) 36 d) 42 Let, Habib’s age is = 6x And Shikha’s age = 4x ARQ, (6x-5)/(4x-5) = 5/3 Or, 18x – 15 = 20x – 25 Or, 2x = 10 Or, x = 5 So, Habib’s age is = 6×5 = 30 year 171. The ratio of two number is 3:4 and their sum is 630. The smaller one of the two number is = a) ৩৬০ b) ২৭০ c) ১৮০ d) ১২০ Let, The numbers are 3x and 4x ATQ, 3x+4x = 630 Or, 7x = 630 Or, x = 90 Smaller number = 3x = 3×90 = 270   172. If x:y =5:3 , then (8x-5y) : (8x +5y) = a) 5 : 11 b) 6 : 5 c) 5 : 6 d) 3 : 8 $$\begin{gathered} \frac{x}{y}=\frac{5}{3} \\ \Rightarrow \frac{8x}{5y}=\frac{5\times 8}{3\times 5} \\ \Rightarrow \frac{8x -5y}{8x+5y}=\frac{40-15}{40+15} \\ \Rightarrow \frac{8x-5y}{8x +5y}=\frac{25}{55} \\ \Rightarrow \frac{8x-5y}{8x+5y}=\frac{5}{11} \end{gathered}$$ 173. The average height of girls in a class is 5 ft and that of boys is 5.7 ft. If the average height of the students in class is 5.5 ft what could be the possible strength of boys and girls respectively in the class: a) 50, 20 b) 30, 20 c) 20, 30 d) 60, 50 50b+57g= 55(b+g) Or, 5b= 2g Or, b:g = 2:5 Now, Summation of age would be multiple of 7. Option A: 50+20= 70; multiple of 7   174. If the ratio of speed of doing work of three persons is 1:3:5. what is the ratio of time taken by these people to do the same amount of work? a) 15:5:3 b) 15:5:7 c) 3:15:5 d) 15:3:5 Time taken by three = 1:1/3:1/5 = 15:5:3 175. If A and B are in the ratio 3:4, and B and C in the ratio 12:13, then A and C will be in the ratio- a) 3:13 b) 36:13 c) 13:9 d) 9:13 (A/B) × (B/C) = (3/4) × (12/13) Or, A/C = 36/52 = 9:13 176. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number? a) 2:5 b) 5:3 c) 5:3 d) 7:3 Exp: Let, 40% of A=(2/3)B Then, 40A/100=2B/3 Or, 2A/5=2B/3 Or, A/B=(2/3 × 5/2)=5/3 So, A:B=5:3. 177. The ratio between the perimeter and the breadth of a rectangle is: 5:1. the area of the rectangle is 216 cm2, what is the length of the rectangle? a) 18 cm b) 24 cm c) 16 cm d) none of these   2(l + b)=     5/1 Or, 2l + 2b = 5b Or, 3b = 2l Or, b = 2l/3 Then, Area = 216 cm2 Or, l x b = 216 Or, l x 2l/3 = 216 Or, l2 = 324 Or, l = 18 cm. 178. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is a) 45:56 b) 45:51 c) 47:36 d) 47:51 Let, The CP be 100. Hence, SP=100+12% of 100=112 If the marked price be X, then 90% of X=112 Or, x= (112×100)/90 Or, x = 1120/90 Hence, Required ratio =100:1120/90=900:1120=45:56   179. In a 729 litres mixture of milk and water, the ratio of milk to water is 7:2. To get a new mixture containing milk and water in the ratio 7:3, the amount of water to be added is- a) 71 litres b) 81 litres c) 56 litres d) 50 litres Quantity of milk in 729 litre of mixture = 7X729/9 = 567 litre Quantity of water = 729-567 = 162 litre. Let x litre of water be added to become ratio 7:3. Or, 7/3 = 567/(162+x) Or, 162×7 +7x = 567×3 Or, 7x = 1701-1134 = 567 Or, x = 567/7 = 81 litre water is to be added. 180. In what ratio must a grocer mix two varieties of pulses costing Tk 15 and Tk 20 per kg respectively so as to get a mixture worth Tk 16.50 kg? a) 3:7 b) 5:7 c) 7:3 d) 7:5 181. Three partners shared the profit in a business in the ratio 5:7:8. They had partnered for 14 months,8 months and 7 months respectively. What was the ratio of their investments? a) 5:7:8 b) 20:49:67 c) 38:28:21 d) None of these Let their investments be x for 14 months, y for 8 months and z for 7 months respectively. Then, 14x : 8y : 7z = 5 : 7 : 8. Now, 14x/8y = 5/7 Or, 98x = 40y Or, y = 49x/20 And, 14x/7z = 5/8 Or, 112x = 35z Or, z = 112x/35 = 16x/5 So x : y : z = x : 49x/20 : 16x/5 —- (Multiple by 20) Or, x : y : z = 20 : 49 : 64   182. In a mixture, the ratio of the milk and water is 6: 5. When 22 liter mixture is replaced by water, the ratio becomes 9:13. Find the quantity of water after replacement. a) 62 liter b) 50 liter c) 40 liter d) 52 liter Let milk  = 6x, water = 5x ATQ, 6x – 22 × 6/11 : 5x – 22 × 5/11    + 22 = 9 : 13 Or, 6x – 12 : 5x – 10 + 22 = 9 : 13 Or, 13 (6x – 12) = 9 (5x + 12) Or, 78x – 156 = 45x + 108 Or, 78x – 45x = 156 + 108 Or, 33x = 264 Or, x = 8 Water after replacement = 5 × 8 – 10 + 22 = 40 + 22 = 52 litre 183. The ratio of the speed of boat in still water to the speed of stream is 16:5. A boat goes 16.5 km in 45 minute upstream, find the time taken by boat to cover the distance of 17.5 km downstream. a) 30 minutes b) 25 minutes c) 50 minutes d) 45 minutes 184. Three boys have marbles in the ratio of 19:5:3. If the boy with the least number has 9 marbles. how many marbles does the boy with the greatest number have? a) 57 b) 33 c) 27 d) 81 Smaller ratio 3 = 9 So, Smaller ratio 1 = 9/3 = 3 Now, Highest ratio 19 = 19×3 = 57 185. In a club 50% of the male voters and 80% of the female voters voted for candidate A. If candida A received 70% of the total votes, what is the ratio of male to female voters? a) 1/3 b) ¾ c) 1/4 d) 1/2 Male voter = x Female voter = y 50% of x + 80% of y = 70% of (x+y) 50x/100 + 80y/100 = 70(x+y)/100 50x + 80y = 70x + 70y 80y – 70y= 70x – 50x 10y = 20x x/y = 10/20 = ½ Commence Meaning: শুরু করা , শুরু হওয়া Synonyms: Begin, Enter, kick off Antonyms: Conclude, Eend, Finish Example: The court commenced criminal proceedings. Enumerate Meaning: গণনা করা , পরপর উল্লেখ করা Synonyms: Detail, Itemize, Recite Antonyms: generalize Example: Let me enumerate my reasons for doing this. 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 BCS Bank বেসরকারি শিক্ষক নিবন্ধন কলেজ বেসরকারি শিক্ষক নিবন্ধন স্কুল Govt. 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