0
70

# Ratio and Proportion Questions for SSC CHSL and MTS

Here you can download the Ratio and Proportion Questions for SSC CHSL and MTS PDF with solutions by Cracku. These are very important practice questions prepared by various sources also based on previous year papers. Utilize this Ratio and Proportion questions and answers PDF to make practice for the SSC CHSL and MTS exams. You can find some difficult questions from ratio and proportions which help you to test yourself and practice. So you can click on the below link to download the PDF for reference and do more practice.

Question 1: A incomes of A and B are in the ratio 3:4 ,and their expenditures are in the ratio 9:5. If the income of A is equal to three times the expenditure of B, then what is the ratio of the savings of A and B?

a) 5:2

b) 3:5

c) 5:3

d) 2:5

Solution:

Let the income of A and B is 3x and 4x and Expenditure is 9y and 5y respectively

Given,

The income of A = 3 times the expenditure of B

i.e; $3x=3\times\ 5y$

i.e; $x=5y$

As we know, Saving = Income – expenditure

Saving of A = 3x – 9y = 15y – 9y = 6y

Saving of B = 4x – 5y = 20y – 5y = 15y

Required Ratio = 6 : 15

i.e; 2 : 5

Hence, Option D is correct.

Question 2: A money was distributed among A, B and C in the ratio of 5:6:7 respectively. If B gave Rs. 400 to C, then the ratio among the distribution of A, B and C will be 2:3:4. Find out the sum of the initial money of A and C.

a) 7,200

b) 14,000

c) 8,400

d) 11,200

Solution:

Let the initial ratio of money is 5x, 6x and 7x.

According to the question,

$\frac{6x-400}{7x+400}=\ \frac{3}{4}$

$24x-1600=21x+1200\$

$=\frac{2800}{3}$

Sum of initial money of A and C is 12x.

so, $:\ \frac{2800}{3}\times\ 12$

i.e; Rs.11200

Question 3: Two numbers are, respectively, 17% and 50% more than a third number. The ratio of the two numbers is:

a) 39:50

b) 50:39

c) 59:39

d) 39:59

Solution:

Let the third number is 100

given in question,

First number is 17% more than 3rd number

i.e; $\left(\frac{17}{100}\times\ 100\right)+100=117$

Second number is 50% more than 3rd number

i.e; $\left(\frac{50}{100}\times\ 100\right)+100=150$

Required ratio = $\frac{117}{150}$

i.e; 39 : 50

Hence, Option A is correct

Question 4: A certain sum is divided among A, B, C and D such that the ratio of the shares is A : B : C : D = 4 : 12 : 30 : 45. If the difference between the shares of A and D is ₹5,535, then the total sum (in ₹) is:

a) 12785

b) 13550

c) 12285

d) 11000

Solution:

Ratio of shares of A, B, C and D is 4 : 12 : 30 : 45 respectively.

Let the shares of A, B, C and D are 4p, 12p, 30p and 45p respectively.

The difference between the shares of A and D is ₹5,535.

45p – 4p = 5535

41p = 5535

p = 135

Total sum = 4p + 12p + 30p + 45p

= 91p

= 91 x 135

= ₹12285

Hence, the correct answer is Option C

Question 5: Fourth proportion to 12, 18, 6 is equal to the third proportion to 4, k. What is the value of k?

a) 6

b) $4\sqrt{3}$

c) 6.5

d) 4

Solution:

Let the fourth proportion to 12, 18, 6 is ‘t’.

12 x t = 18 x 6

t = 9

According to the problem ‘t’ is the third proportion to 4, k.

$\frac{4}{k}$ = $\frac{k}{t}$

$\frac{4}{k}$ = $\frac{k}{9}$

k$^2$ = 36

k = 6

Hence, the correct answer is Option A

Question 6: Monthly salaries of Anil and Kumud are in the ratio 19 : 17. If Anil and Kumud get salary hike of ₹2000 and ₹1000 respectively, then the ratio in their salaries become 8 : 7. What is the present salary of Kumud(in ₹)?

a) 38000

b) 18000

c) 34000

d) 35000

Solution:

Monthly salaries of Anil and Kumud are in the ratio 19 : 17.

Let the monthly salaries of Anil and Kumud are 19p and 17p respectively.

Anil and Kumud get salary hike of ₹2000 and ₹1000 respectively, then the ratio in their salaries become 8 : 7.

$\frac{19p+2000}{17p+1000}=\frac{8}{7}$

133p + 14000 = 136p + 8000

3p = 6000

p = 2000

Present salary of Kumud = 17p = ₹34000

Hence, the correct answer is Option C

Question 7: If p is the third proportional to 3, 9, then what is the fourth proportional to 6, p, 4?

a) $\frac{3}{2}$

b) 10

c) 18

d) $2\sqrt{3}$

Solution:

p is the third proportional to 3, 9.

$\frac{p}{9}=\frac{9}{3}$

p = 27

Let the ‘n’ is the fourth proportional of 6, p, 4.

n x 6 = p x 4

n x 6 = 27 x 4

n = 18

Fourth proportional of 6, p, 4 is 18.

Hence, the correct answer is Option C

Question 8: When x is subtracted from each of the numbers 54, 49, 22 and 21, the numbers so obtained are in proportion. The ratio of (8x – 25) to (7x – 26) is:

a) 5 : 4

b) 27 : 26

c) 29 : 24

d) 15 : 13

Solution:

According to the problem,

$\left(54-x\right)\left(21-x\right)=\left(49-x\right)\left(22-x\right)$

$1134-75x+x^2=1078-71x+x^2$

$4x=56$

$x=14$

$\left(8x-25\right):\left(7x-26\right)=8\left(14\right)-25\ :\ 7\left(14\right)-26$

= 87 : 72

= 29 : 24

Hence, the correct answer is Option C

Question 9: If x is subtracted from each of 24, 40, 33 and 57, the numbers, so obtained are in proportion. The ratio of (5x + 12) to (4x + 15) is:

a) 7:4

b) 4:3

c) 14:13

d) 7:5

Solution:

According to the problem,

$\left(24-x\right)\left(57-x\right)=\left(40-x\right)\left(33-x\right)$

$1368-81x+x^2=1320-73x+x^2$

$8x=48$

$x=6$

The ratio of (5x + 12) to (4x + 15) = 5(6) + 12 : 4(6) + 15

= 42 : 39

= 14 : 13

Hence, the correct answer is Option C

Question 10: Two numbers are in the ratio 2 : 3. If 5 is subtracted from the first number and six is added to the second number, then the ratio becomes 5 : 12. What would the ratio become when eight is added to each number?

a) 19 : 14

b) 14 : 19

c) 11 : 14

d) 14 : 11

Solution:

Two numbers are in the ratio 2 : 3.

Let the two numbers are 2p and 3p respectively.

According to the problem,

$\frac{2p-5}{3p+6}=\frac{5}{12}$

24p – 60 = 15p + 30

9p = 90

p = 10

Required ratio = $\frac{2p+8}{3p+8}=\frac{2\left(10\right)+8}{3\left(10\right)+8}=\frac{28}{38}=\frac{14}{19}$

Hence, the correct answer is Option B

Question 11: The ratio of monthly incomes of A and B is 4 : 5 and that of their monthly expenditures is 3 : 8. If the income of A is equal to the expenditure of B, then what is the ratio of savings of A and B?

a) 3:8

b) 2:5

c) 8:3

d) 5:2

Solution:

The ratio of monthly incomes of A and B is 4 : 5.

Let the monthly incomes of A and B are 4p and 5p respectively.

The income of A is equal to the expenditure of B.

Monthly expenditure of B = 4p

The ratio of monthly expenditures of A and B is 3 : 8.

Monthly expenditure of A = $\frac{3}{8}\times$4p = $\frac{3}{2}$p

The ratio of savings of A and B = (4p – $\frac{3}{2}$p) : (5p – 4p)

= $\frac{5}{2}$p : p

= 5 : 2

Hence, the correct answer is Option D

Question 12: The ratio of two numbers A and B is 5 : 8. If 5 is added to each of A and B, then the ratio becomes 2 : 3. The difference in A and B is:

a) 15

b) 20

c) 12

d) 10

Solution:

The ratio of two numbers A and B is 5 : 8.

Let the two numbers are 5p and 8p respectively.

According to the problem,

$\frac{5p+5}{8p+5}=\frac{2}{3}$

15p + 15 = 16p + 10

p = 5

Difference in A and B = 8p – 5p

= 3p

= 3 x 5

= 15

Hence, the correct answer is Option A

Question 13: What is the third proportional to 16 and 24?

a) 28

b) 34

c) 32

d) 36

Solution:

Let the third proportional of 16 and 24 = a

$\Rightarrow$  $\frac{16}{24}=\frac{24}{a}$

$\Rightarrow$  a = 36

$\therefore\$The third proportional of 16 and 24 = 36

Hence, the correct answer is Option D

Question 14: The salaries of Vipin and Dinesh are in the ratio 5 : 8. If the salary of each is increased by ₹ 4,800, then new ratio becomes 7 : 10. What is Vipin’s salary ?

a) ₹ 13,000

b) ₹ 12,000

c) ₹ 12,500

d) ₹ 10,000

Solution:

Given, ratio of salaries of Vipin and Dinesh = 5 : 8

Let the salaries of Vipin and Dinesh are 5p and 8p respectively.

If the salary of each is increased by ₹ 4,800, then new ratio becomes 7 : 10.

$\Rightarrow$  $\frac{5p+4800}{8p+4800}=\frac{7}{10}$

$\Rightarrow$  $50p+48000=56p+33600$

$\Rightarrow$  $6p=14400$

$\Rightarrow$  $p=2400$

$\therefore\$Salary of Vipin = 5p = 5 x 2400 = ₹ 12,000

Hence, the correct answer is Option B

Question 15: If a : b = 3 : 4, find the value of (7a – 4b) : (8a + 4b).

a) 1 : 8

b) 2 : 3

c) 3 : 8

d) 2 : 5

Solution:

Given, a : b = 3 : 4

$\Rightarrow$  $\frac{a}{b}=\frac{3}{4}$

$\Rightarrow$  $\frac{4a}{4b}=\frac{3}{4}$

$\Rightarrow$  $4b=\frac{16a}{3}$

(7a – 4b) : (8a + 4b) $=\frac{7a-4b}{8a+4b}$

$=\frac{7a-\frac{16a}{3}}{8a+\frac{16a}{3}}$

$=\frac{\frac{21a-16a}{3}}{\frac{24a+16a}{3}}$

$=\frac{5a}{40a}$

$=\frac{1}{8}$

$=$ 1 : 8

Hence, the correct answer is Option A

Question 16: A sum of ₹1,260 is distributed between Ravi and Mohan. If the shares of Ravi and Mohan are in ratio 5 : 4, then the shares of Ravi and Mohan are respectively:

a) ₹680 and ₹580

b) ₹800 and ₹460

c) ₹700 and ₹560

d) ₹750 and ₹510

Solution:

Given,  Sum = ₹1,260

Ratio of shares of Ravi and Mohan = 5 : 4

Let the share of Ravi and Mohan are 5p and 4p respectively.

$\Rightarrow$  5p + 4p = 1260

$\Rightarrow$  9p = 1260

$\Rightarrow$  1p = 140

Share of Ravi = 5p = 5 x 140 = ₹700

Share of Mohan = 4p = 4 x 140 = ₹560

Hence, the correct answer is Option C

Question 17: The incomes of two persons P and Q are in the ratio 5 : 6. If each of them saves ₹ 200 per month, the ratio of their expenditures is 3 : 4. Find the income of Q.

a) ₹ 800

b) ₹ 750

c) ₹ 740

d) ₹ 600

Solution:

Ratio of expenditure of P and Q = 3 : 4

Let the expenditure of P and Q are 3a and 4a respectively

Both of them save ₹ 200 per month

Ratio of income of P and Q = 5 : 6

$\Rightarrow$ $\frac{200+3a}{200+4a}=\frac{5}{6}$

$\Rightarrow$ $1200+18a=1000+20a$

$\Rightarrow$ $2a=200$

$\Rightarrow$ $a=100$

$\therefore\$Income of Q = Savings + Expenditure = 200 + 4a = 200 + 4(100) = 200 + 400 = ₹ 600

Hence, the correct answer is Option D

Question 18: In a 56 liters mixture of milk and water, the ratio of milk to water is 5 : 2. In order to make the ratio of milk to water  7 : 2, some quantity of milk is to be added to the mixture. The quantity of the milk present in the new mixture will be:

a) 16 liters

b) 40 liters

c) 48 liters

d) 56 liters

Solution:

Given,

Ratio of milk and water in a 56 liters of mixture = 5 : 2

$=$>  Quantity of milk in 56 liters mixture = $\frac{5}{5+2}\times56=40$

$=$>  Quantity of water in 56 liters mixture = $\frac{2}{5+2}\times56=16$

Let the quantity of milk added to make the mixture in the ratio  7 : 2 = $a$

$=$>  $\frac{40+a}{16}=\frac{7}{2}$

$=$>  $40+a=56$

$=$>  $a=16$

$\therefore\$Quantity of milk present in new mixture = 40+a = 40+16 = 56 liters

Hence, the correct answer is Option D

Question 19: The ratio of tables and chairs in a room is 7 : 9. If there are 560 tables and chairs in the room, then what is the number of chairs ?

a) 397

b) 489

c) 315

d) 463

Solution:

Given, Total number of tables and chairs = 560

Ratio of tables and chairs in the room = 7 : 9

Let the number of tables and chairs in the room are 7p and 9p respectively

$=$>   7p + 9p = 560

$=$>   16p = 560

$=$>    1p = 35

$\therefore\$The number of chairs in the room = 9p = 9(35) = 315

Hence, the correct answer is Option C

Question 20: The average price of three items is $₹ 14,265.$ If their prices are in the ratio 7 : 9 : 11, then the price of the costliest item is:

a) $₹ 16,235$

b) $₹ 14,875$

c) $₹ 17,435$

d) $₹ 19,875$

The average price of three items is $₹ 14,265$
Costliest item of the three = $\frac{11}{7+9+11}\times42,795$ = $\frac{11}{27}\times42795$ = $₹ 17,435$