# Ratio and Proportion Questions for SSC MTS

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**Question 1:Â **How much should be added to each term of 4 : 7 so that it becomes 2 : 3?

a)Â 2

b)Â 3

c)Â 4

d)Â 1

**1)Â AnswerÂ (A)**

**Solution:**

Let $x$ is added to the each term of 4 : 7

According to the problem,

$\frac{4+x}{7+x}=\frac{2}{3}$

$=$> Â $12+3x=14+2x$

$=$> Â $3x-2x=14-12$

$=$> Â $x=2$

Hence, the correct answer is Option A

**Question 2:Â **If $a : b = 3 : \sqrt 5$, then the value of (2a + b) : (3a â€” 2b) is:

a)Â $\frac{1}{64} (64 + 21 \sqrt 5)$

b)Â $\frac{1}{61} (64 + 21 \sqrt 5)$

c)Â $\frac{1}{62} (64 + 21 \sqrt 5)$

d)Â $\frac{1}{63} (64 + 21 \sqrt 5)$

**2)Â AnswerÂ (B)**

**Solution:**

Given,Â $a : b = 3 : \sqrt 5$

$=$> Â $\frac{a}{b}=\frac{3}{\sqrt{5}}$

$=$> Â $a=\frac{3}{\sqrt{5}}b$

$\therefore\ $(2a + b) : (3a – 2b) = $\frac{2a+b}{3a-2b}$

$=\frac{2\left(\frac{3}{\sqrt{5}}b\right)+b}{3\left(\frac{3}{\sqrt{5}}b\right)-2b}$

$=\frac{6b+\sqrt{5}b}{9b-2\sqrt{5}b}$

$=\frac{6+\sqrt{5}}{9-2\sqrt{5}}\times\frac{9+2\sqrt{5}}{9+2\sqrt{5}}$

$=\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{9^2-\left(2\sqrt{5}\right)^2}$

$=\frac{54+12\sqrt{5}+9\sqrt{5}+2\left(5\right)}{81-20}$

$=\frac{1}{61}\left(64+21\sqrt{5}\right)$

Hence, the correct answer is Option B

**Question 3:Â **What number must be added to each of the numbers 8, 13, 26 and 40 so that the numbers obtained in this order are in proportion?

a)Â 3

b)Â 2

c)Â 1

d)Â 4

**3)Â AnswerÂ (B)**

**Solution:**

Let the number which is added to make the numbers 8, 13, 26, 40 are in proportion = $x$

$=$>Â 8+$x$, 13+$x$, 26+$x$, 40+$x$ are in proportion

$=$> Â $\frac{8+x}{13+x}=\frac{26+x}{40+x}$

$=$> Â $\left(8+x\right)\left(40+x\right)=\left(26+x\right)\left(13+x\right)$

$=$> Â $320+8x+40x+x^2=338+26x+13x+x^2$

$=$> Â $320+48x=338+39x$

$=$> Â $48x-39x=338-320$

$=$> Â $9x=18$

$=$> Â $x=2$

$\therefore\ $The number which is added to make the numbers 8, 13, 26, 40 are in proportion = 2

Hence, the correct answer is Option B

**Question 4:Â **If an amount of $â‚¹ 800$ is distributed between Ravi, Mohan and Govind in the proportions 2 : 5 : 3, then the sum of the shares of Mohan and Govind,is:

a)Â $â‚¹ 400$

b)Â $â‚¹ 640$

c)Â $â‚¹ 560$

d)Â $â‚¹ 240$

**4)Â AnswerÂ (B)**

**Solution:**

Given,

$â‚¹ 800$ is distributed between Ravi, Mohan and Govind in the proportions 2 : 5 : 3

$=$>Â Share of Mohan =Â $=\frac{5}{2+5+3}\times\ 800=\frac{5}{10}\times800=â‚¹ 400$

$=$>Â Share of Govind =Â $=\frac{3}{2+5+3}\times\ 800=\frac{3}{10}\times800=â‚¹ 240$

$\therefore\ $Sum of the shares of Mohan and Govind = 400 + 240 =â‚¹ 640

Hence, the correct answer is Option B

**Question 5:Â **The fourth proportional to 10, 12, 15 is:

a)Â 20

b)Â 18

c)Â 24

d)Â 22

**5)Â AnswerÂ (B)**

**Solution:**

Let the fourth proportional to 10, 12, 15 = $d$

$=$> Â $\frac{10}{12}=\frac{15}{d}$

$=$> Â $10d=180$

$=$> Â $d=18$

Hence, the correct answer is Option B

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**Question 6:Â **Two numbers are respectively 25% and 65% more than a third number. The ratio of the two numbers is:

a)Â 16 : 17

b)Â 25 : 42

c)Â 25 : 33

d)Â 16 : 19

**6)Â AnswerÂ (C)**

**Solution:**

Let the third number = a

Given,

First number is 25% more than third number

$=$> First number =Â $\frac{125}{100}a$

Second number is 65% more than third number

$=$> Second number =Â $\frac{165}{100}a$

$\therefore\ $Ratio of first and second number = $\frac{125}{100}a:\frac{165}{100}a$ = $25:33$

Hence, the correct answer is Option C

**Question 7:Â **Dividing the amount â‚¹18,144 among three people A, B, C in the ratio 3 : 5 : 8, the amount B gets more than A, is:

a)Â â‚¹2,268

b)Â â‚¹2,386

c)Â â‚¹2,178

d)Â â‚¹2,464

**7)Â AnswerÂ (A)**

**Solution:**

Given, Total amount = â‚¹18,144

Ratio of amounts of A,B,C = 3 : 5 :8

Let the amounts of A,B,C are 3p, 5p, 8p respectively

$=$>Â 3p + 5p + 8p = 18144

$=$>Â 16p = 18144

$=$> Â p = 1134

$\therefore\ $The amount that B gets more than A = 5p – 3p = 2p = 2(1134) =Â â‚¹2,268

Hence, the correct answer is Option A

**Question 8:Â **If 2145 : x :: 3003 : 42, then the value of y so that x : 2508 :: y : 11704, is:

a)Â 156

b)Â 96

c)Â 212

d)Â 140

**8)Â AnswerÂ (D)**

**Solution:**

Given,Â 2145 : x :: 3003 : 42

$=$> Â $\frac{2145}{x}=\frac{3003}{42}$

$=$> Â $x=\frac{2145\times42}{3003}$

$=$> Â $x=30$

x : 2508 :: y : 11704

$=$> Â $\frac{x}{2508}=\frac{y}{11704}$

$=$> Â $\frac{30}{2508}=\frac{y}{11704}$

$=$> Â $y=\frac{30\times11704}{2508}$

$=$> Â $y=140$

Hence, the correct answer is Option D

**Question 9:Â **If 22% of x = 30% of y, then y : x is equal to:

a)Â 15 : 14

b)Â 11 : 15

c)Â 15 : 11

d)Â 17 : 16

**9)Â AnswerÂ (B)**

**Solution:**

Given,Â 22% of x = 30% of y

$=$>Â $\frac{22}{100}\times x=\frac{30}{100}\times y$

$=$>Â $\frac{y}{x}=\frac{22}{30}$

$=$> Â $\frac{y}{x}=\frac{11}{15}$

$=$> Â $y:x=11:15$

**Question 10:Â **The sum of three numbers is 79. If the ratio of the first number to the second number is 4 : 7 and that of the second number to the third number is 4 : 5, then the second number is:

a)Â 12

b)Â 28

c)Â 15

d)Â 35

**10)Â AnswerÂ (B)**

**Solution:**

Let the three numbers are a, b, c

Given, Sum of the numbers = 79

Ratio of first number to second number = 4 : 7

$=$>Â a : b = 4 : 7

$=$> a : b = 16 : 28

Ratio of second number to third number = 4 : 5

$=$>Â b : c = 4 : 5

$=$> b : c = 28 : 35

$=$> a : b : c = 16 : 28 : 35

$\therefore\ $Second number =Â $\frac{28}{79}\times79$ = 28

Hence, the correct answer is Option B

**Question 11:Â **What x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion? What is the mean proportional between the numbers (x + 1) and (3x + 1)?

a)Â 12

b)Â 9

c)Â 15

d)Â 10

**11)Â AnswerÂ (C)**

**Solution:**

If x is added to each of numbers,Â the numbers so obtained in this order are in proportion

so, $\frac{10 + x}{16 + x} = \frac{22 + x}{32 + x}$

(10 + x)(32 + x) =Â (16 + x)(22 + x)

320 + 10x + 32x + $x^2 = 352 + 16x + 22x + x^2$

320 + 42x = 352 + 38x

4x = 32

x = 8

(x + 1) = 8 + 1 = 9

(3x + 1) = 24 + 1 = 25

Mean proportional = $\sqrt{9 \times 25}$ = 15

**Question 12:Â **If A : B = 3 : 5, and B : C = 2 : 3, then A : B : C is equal to:

a)Â 3 : 8 : 6

b)Â 3 : 7 : 3

c)Â 6 : 10 : 15

d)Â 6 : 15 : 10

**12)Â AnswerÂ (C)**

**Solution:**

A : B = 3 : 5Â —(1)Â and B : C = 2 : 3 —(2)

To find the A :Â B :C, we will equal the common term so,

equation (1) multiply by 2 and equation (2) multiply by 5,

A : B = 6 ; 10

B : C = 10 : 15

A : B : C = 6 : 10 : 15

**Question 13:Â **The ratio of boys and girls in a groupis 7 : 6. If 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls becomes 4 : 3. Whatis the total number of boys and girls initially in the group?

a)Â 117

b)Â 78

c)Â 91

d)Â 104

**13)Â AnswerÂ (D)**

**Solution:**

The ratio of boys and girls in a group is 7 : 6.

Let the boys be 7x and girls be 6x.

WhenÂ 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls = 4 : 3

$\frac{7x + 4}{6x -3} = \frac{4}{3}$

21x +Â 12 = 24x -12

3x = 24

x = 8

Initially boys and girlsÂ = 7xÂ + 6xÂ = 13x = 13 $\times$ 8 = 104

**Question 14:Â **If an amount of Rs.990 is divided among A, B and C in the ratio of 3 : 4 : 2, then B will get:

a)Â Rs. 247.5

b)Â Rs. 440

c)Â Rs. 110

d)Â Rs. 350

**14)Â AnswerÂ (B)**

**Solution:**

Ratio of the A, B and C = 3 : 4 : 2

Amount = 990

Share of B = $\frac{4}{3 +Â 4 + 2} \times 990Â = \frac{4}{9} \times 990 = Rs.440

**Question 15:Â **Two numbers are in the ratio 5 : 7. If the first numberis 20, then the second number will be:

a)Â 8

b)Â 22

c)Â 28

d)Â 18

**15)Â AnswerÂ (C)**

**Solution:**

Let the two numbers be 5x and 7x.

According to question,

5x = 20

x = 4

Second number = 7 $\times$ 4 = 28

**Question 16:Â **The total number of students in a class is 65. If the total number of girls in the class is 35, then the ratio of the total number of boys to the total number of girls is:

a)Â 6:7

b)Â 7:6

c)Â 13:7

d)Â 7:13

**16)Â AnswerÂ (A)**

**Solution:**

The ratio of the total number of boys to the total number of girls = 65 : 35 = 13 : 7

**Question 17:Â **The sum of the squares of 3 natural numbers is 1029, and they are in the proportion 1 : 2 : 4. The difference between greatest number and smallest number is:

a)Â 15

b)Â 21

c)Â 31

d)Â 18

**17)Â AnswerÂ (B)**

**Solution:**

Let the smallest number be x.

Numbers are x, 2x, 4x.

The sum of the squares of 3 natural numbers = 1029

$x^2 + (2x)^2 +Â (4x)^2 = 1029$

$x^2 +Â 4x^2 + 16x^2 = 1029$

$x^2 = 1029/21$

$x^2 = 49$

$x = 7$

Smallest number = 7

Greatest number = 4x = 4 $\times$ 7 = 28

The difference between greatest number and smallest number = 28 – 7 = 21

**Question 18:Â **25 litres of a mixture contains 30%of spirit and rest water. If 5 litres of water be mixed in it, the percentage of spirit in the new mixture is :

a)Â $45\%$

b)Â $33 \frac{1}{3}\%$

c)Â $25 \%$

d)Â $12 \frac{1}{2} \%$

**18)Â AnswerÂ (C)**

**Solution:**

Quantity of spirit = $25\times \frac{30}{100} = 7.5$

Quantity of water = 25 – 7.5 = 17.5

After mixed up quantity of mixture = 25 + 5 = 30

Percentage of spirit =Â $\frac{7.5}{30} \times 100$ = 25%

**Question 19:Â **In wallet, there are notes of the denominations â‚¹10 and â‚¹50. The total number of notes is 12. The number of â‚¹10 and 50 notes are in the ratio of 1 : 2. Total money in the wallet is:

a)Â â‚¹ 360

b)Â â‚¹ 280

c)Â â‚¹ 110

d)Â â‚¹ 440

**19)Â AnswerÂ (D)**

**Solution:**

The ratio of the number ofÂ â‚¹10 andÂ â‚¹50 notes = 1 :Â 2

The total number of notes = 12

The number of â‚¹10 notes = $\frac{1}{1 + 2} \times 12 = 4

Money from theÂ â‚¹10 notes = 4 $\times$ 10 = Rs.40

The number of â‚¹50 notes = 12 – 4 = 8

Money from the â‚¹50 notes = 8 $\times$ 50 = Rs.400

Total money in the wallet = 40 + 400 = Rs.440

**Question 20:Â **A certain amount is divided among Sunita, Amit and Vibha in the ratio of 2 : 3 : 4. If Vibha gets â‚¹14,416, then the total amount is:

a)Â â‚¹16,219

b)Â â‚¹3,604

c)Â â‚¹43,248

d)Â â‚¹32,436

**20)Â AnswerÂ (D)**

**Solution:**

Ratio of the amount ofÂ Sunita, Amit and Vibha =Â 2 : 3 : 4

Let the amount of Sunita, Amit and Vibha be 2x, 3x and 4x.

Amount of Vibha = 14416

4x = 14416

x =Â 14416/4 = 3604

Total amount = 2x + 3x + 4x = 9x

= 9 $\times $ 3604 = Rs.32436

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