Ratio and Proportion Questions for SSC CHSL and MTS

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Download Ratio and Proportion Questions for SSC CHSL and MTS

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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

1) Answer (D)

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

2) Answer (D)

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

3) Answer (A)

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

4) Answer (C)

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

5) Answer (A)

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

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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

6) Answer (C)

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) $2\sqrt{3}$

7) Answer (C)

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

8) Answer (C)

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

9) Answer (C)

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

10) Answer (B)

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

11) Answer (D)

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

12) Answer (A)

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

13) Answer (D)

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

14) Answer (B)

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

15) Answer (A)

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

16) Answer (C)

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

17) Answer (D)

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

18) Answer (D)

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

19) Answer (C)

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) $₹ 19,875$

20) Answer (C)

Solution:

Given,

The average price of three items is $₹ 14,265$

Sum of the price of three items = 14265 x 3 = 42795

Costliest item of the three = $\frac{11}{7+9+11}\times42,795$ = $\frac{11}{27}\times42795$ = $₹ 17,435$

Hence, the correct answer is Option C

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