# Be thorough with ratio and proportion problems

Published: Published Date - 11:59 PM, Thu - 25 August 22

**Hyderabad:** This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

**1. A person whose monthly income is Rs 363 spends an amount equal to his 3 months income in 4 months. After one year he distributes his savings among his three sons in such a way that the share of the eldest son is double the share of his second son and three times the share of his third son. Find the share of his youngest son?**

a) Rs 198 b) Rs 196 c) Rs 195 d) Rs 192

Ans: a

Solution: Income of 1 month = Rs 363

Income of 3 months = 363 × 3 = Rs 1089

Expense of 4 months = Rs 1089

Savings of 4 months = 363 × 4 – 1089

= 1452 – 1089

= Rs 363

Savings of 12 months = 363 × 3 = Rs 1089

Ratio of share of sons = 1 : 1/2 : 1/3

= 6 : 3 : 2

Share of youngest son = 2 –>; ?

11 –>; 1089

= Rs 198

**2. Meena, Chaitanya and Priyanka rented a car in partnership for Rs 2,100. If they used car for 24 hours, 36 hours and 66 hours respectively, how much rent did Chaitanya pay?**

a) Rs 650 b) Rs 625 c) Rs 600 d) Rs 615

Ans: c

Solution: Ratio of rent = 24 : 36 : 66

= 4 : 6 : 11

21 –>; 2100

6 –>; ?

= Rs 600

**3. Ratio of three numbers is 3 : 5 : 4 and sum of squares of the numbers is 200. Find the difference between the largest and the smallest number?**

a) 1 b) 2 c) 3 d) 4

Ans: d

Solution: (3x)² (5x)² (4x)² = 200

50x² = 200

x² = 40

x = 2

5x – 3x = 2x

= 2 × 2

= 4

**4. The difference of two numbers is equal to 30% of their sum. Find the ratio of the larger number to the smaller number.**

a) 7 : 5 b) 13 : 7 c) 11 : 7 d) 9 : 5

Ans: b

Solution: (x – y ) = (x y) × 30/100

10 (x – y) = 3(x y)

7x = 13y

x : y = 13 : 7

**5. If a³ b³ : a³ – b³ = 185 : 158 then a : b =**

a) 7 : 3 b) 2 : 3 c) 10 : 2 d) 5 : 4

Ans: a

Solution:

158a³ 158 b³ = 185a³ – 185b³

185a³ – 158a³ = 158b³ 185b³

27a³ = 343b³

a³/b³ = 343/27

a/b = 3√343/27

a/b = 7/3 = 7 : 3

**6. Two numbers are 40% and 60% more than the third number respectively. What is the ratio of the first number to the second number?**

a) 5 : 6 b) 6 : 7 c) 7 : 8 d) 8 : 9

Ans: c

Solution: Let the third number = 100

The first number = 140

and second number = 160

140 : 160

= 7 : 8

**7. Income and expenditure of a person are in the ratio of 9 : 5. If the income of the person is Rs 27,000, then find his savings.**

a) Rs 10,000 b) Rs 12,000 c) Rs 11,500 d) Rs 12,700

Ans: b

Solution: 9 –>; 27,000

4 –>; ?

3000 × 4 = Rs 12,000

**8. If a : b = 3 : 4 and d : b = 4 : 3, then find the ratio of a to d.**

a) 9 : 16 b) 16 : 9 c) 4 : 3 d) 3 : 4

Ans: a

Solution: a/b = 3/4 ; b/d = 3/4

a/b × b/d = 3/4 × 3/4

a/d = 9/16

= 9 : 16

**9. If 1/3 of A = 3/4 of B = 1/6 of C, then find the ratio of A : B : C.**

a) 18 : 4 : 9 b) 9 : 18 : 4 c) 9 : 4 : 18 d) 18 : 9 : 4

Ans: c

Solution: A/3 = 3B/4 = C/6

A/9 = B/4 = C/18

A : B : C = 9 : 4 : 18

**To be continued…**

**M. Venkat**

**Director**

**MVK Publications**

**Dilsukhnagar**

**7671002120**