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Ratio and Proportion Questions for SSC MTS

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

a) 2

b) 3

c) 4

d) 1

Solution:

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

According to the problem,

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

$=$>  $12+3x=14+2x$

$=$>  $3x-2x=14-12$

$=$>  $x=2$

Hence, the correct answer is Option A

Question 2: If $a : b = 3 : \sqrt 5$, then the value of (2a + b) : (3a — 2b) is:

a) $\frac{1}{64} (64 + 21 \sqrt 5)$

b) $\frac{1}{61} (64 + 21 \sqrt 5)$

c) $\frac{1}{62} (64 + 21 \sqrt 5)$

d) $\frac{1}{63} (64 + 21 \sqrt 5)$

Solution:

Given,  $a : b = 3 : \sqrt 5$

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

$=$>  $a=\frac{3}{\sqrt{5}}b$

$\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: 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) 3

b) 2

c) 1

d) 4

Solution:

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

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

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

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

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

$=$>  $320+48x=338+39x$

$=$>  $48x-39x=338-320$

$=$>  $9x=18$

$=$>  $x=2$

$\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: If an amount of $₹ 800$ 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) $₹ 400$

b) $₹ 640$

c) $₹ 560$

d) $₹ 240$

Solution:

Given,

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

$=$>  Share of Mohan = $=\frac{5}{2+5+3}\times\ 800=\frac{5}{10}\times800=₹ 400$

$=$>  Share of Govind = $=\frac{3}{2+5+3}\times\ 800=\frac{3}{10}\times800=₹ 240$

$\therefore\$Sum of the shares of Mohan and Govind = 400 + 240 =₹ 640

Hence, the correct answer is Option B

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

a) 20

b) 18

c) 24

d) 22

Solution:

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

$=$>  $\frac{10}{12}=\frac{15}{d}$

$=$>  $10d=180$

$=$>  $d=18$

Hence, the correct answer is Option B

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

a) 16 : 17

b) 25 : 42

c) 25 : 33

d) 16 : 19

Solution:

Let the third number = a

Given,

First number is 25% more than third number

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

Second number is 65% more than third number

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

$\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: Dividing the amount ₹18,144 among three people A, B, C in the ratio 3 : 5 : 8, the amount B gets more than A, is:

a) ₹2,268

b) ₹2,386

c) ₹2,178

d) ₹2,464

Solution:

Given, Total amount = ₹18,144

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

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

$=$>  3p + 5p + 8p = 18144

$=$>  16p = 18144

$=$>   p = 1134

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

Hence, the correct answer is Option A

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

a) 156

b) 96

c) 212

d) 140

Solution:

Given, 2145 : x :: 3003 : 42

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

$=$>  $x=\frac{2145\times42}{3003}$

$=$>  $x=30$

x : 2508 :: y : 11704

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

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

$=$>  $y=\frac{30\times11704}{2508}$

$=$>  $y=140$

Hence, the correct answer is Option D

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

a) 15 : 14

b) 11 : 15

c) 15 : 11

d) 17 : 16

Solution:

Given, 22% of x = 30% of y

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

$=$>  $\frac{y}{x}=\frac{22}{30}$

$=$>  $\frac{y}{x}=\frac{11}{15}$

$=$>  $y:x=11:15$

Question 10: 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) 12

b) 28

c) 15

d) 35

Solution:

Let the three numbers are a, b, c

Given, Sum of the numbers = 79

Ratio of first number to second number = 4 : 7

$=$>  a : b = 4 : 7

$=$> a : b = 16 : 28

Ratio of second number to third number = 4 : 5

$=$>  b : c = 4 : 5

$=$> b : c = 28 : 35

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

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

Hence, the correct answer is Option B

Question 11: 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) 12

b) 9

c) 15

d) 10

Solution:

If x is added to each of numbers, 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) = (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: If A : B = 3 : 5, and B : C = 2 : 3, then A : B : C is equal to:

a) 3 : 8 : 6

b) 3 : 7 : 3

c) 6 : 10 : 15

d) 6 : 15 : 10

Solution:

A : B = 3 : 5 —(1) and B : C = 2 : 3 —(2)
To find the A : 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: 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) 117

b) 78

c) 91

d) 104

Solution:

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

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

When 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 + 12 = 24x -12

3x = 24

x = 8

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

Question 14: 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) Rs. 247.5

b) Rs. 440

c) Rs. 110

d) Rs. 350

Solution:

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

Amount = 990

Share of B = $\frac{4}{3 + 4 + 2} \times 990 = \frac{4}{9} \times 990 = Rs.440 Question 15: Two numbers are in the ratio 5 : 7. If the first numberis 20, then the second number will be: a) 8 b) 22 c) 28 d) 18 15) Answer (C) Solution: Let the two numbers be 5x and 7x. According to question, 5x = 20 x = 4 Second number = 7$\times$4 = 28 Question 16: The total number of students in a class is 65. If the total number of girls in the class is 35, then the ratio of the total number of boys to the total number of girls is: a) 6:7 b) 7:6 c) 13:7 d) 7:13 16) Answer (A) Solution: The ratio of the total number of boys to the total number of girls = 65 : 35 = 13 : 7 Question 17: The sum of the squares of 3 natural numbers is 1029, and they are in the proportion 1 : 2 : 4. The difference between greatest number and smallest number is: a) 15 b) 21 c) 31 d) 18 17) Answer (B) Solution: Let the smallest number be x. Numbers are x, 2x, 4x. The sum of the squares of 3 natural numbers = 1029$x^2 + (2x)^2 + (4x)^2 = 1029x^2 + 4x^2 + 16x^2 = 1029x^2 = 1029/21x^2 = 49x = 7$Smallest number = 7 Greatest number = 4x = 4$\times$7 = 28 The difference between greatest number and smallest number = 28 – 7 = 21 Question 18: 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)$45\%$b)$33 \frac{1}{3}\%$c)$25 \%$d)$12 \frac{1}{2} \%$18) Answer (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 =$\frac{7.5}{30} \times 100$= 25% Question 19: In wallet, there are notes of the denominations ₹10 and ₹50. The total number of notes is 12. The number of ₹10 and 50 notes are in the ratio of 1 : 2. Total money in the wallet is: a) ₹ 360 b) ₹ 280 c) ₹ 110 d) ₹ 440 19) Answer (D) Solution: The ratio of the number of ₹10 and ₹50 notes = 1 : 2 The total number of notes = 12 The number of ₹10 notes =$\frac{1}{1 + 2} \times 12 = 4

Money from the ₹10 notes = 4 $\times$ 10 = Rs.40

The number of ₹50 notes = 12 – 4 = 8

Money from the ₹50 notes = 8 $\times$ 50 = Rs.400

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

Question 20: A certain amount is divided among Sunita, Amit and Vibha in the ratio of 2 : 3 : 4. If Vibha gets ₹14,416, then the total amount is:

a) ₹16,219

b) ₹3,604

c) ₹43,248

d) ₹32,436

Solution:

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

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

Amount of Vibha = 14416

4x = 14416

x = 14416/4 = 3604

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

= 9 $\times$ 3604 = Rs.32436