Solve these ratio and proportion problems

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. The present age of A and B are in the ratio 4 : 5 and after 5 […]

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. The present age of A and B are in the ratio 4 : 5 and after 5 years they will be in the ratio 5 : 6. The present age of A is?
a) 20 years b) 30 years c) 40 years d) 50 years
Ans: a
Solution: Let the present age of A and B be 4x and 5x years respectively,
According to the question,
(4x 5) / (5x 5) = 5/6
=>; 25x 25 = 24x 30
=>; x = 30 – 25 = 5
 A’s present age,
= 4x = 4 × 5 = 20 years

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2. The ratio of the present age of Rohan and Rithika is 2 : 1. The ratio of their age after 30 years will be 7 : 6. What is the present age of Rohan?
a) 6 years b) 18 years c) 12 years d) 24 years
Ans: c
Solution: Let the present age of Rohan and Rithika be 2x and x years respectively.
After 30 years,
(2x 30) / (x 30) = 7/6
=>;12 x 180 = 7x 210
=>;12 x –7x = 210–180
=>; 5 x = 30 =>; 30/5 = 6
Rohan’s present age
= 2x = 2×6 = 12 years

3. My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was?
a) 2 : 5 b) 1 : 5 c) 5 : 2 d) 5 : 1
Ans: b
Solution: My age = x years
My grandfather’s age = 9x years
After 8 years from the present,
9x 16 8 = 3(x 8 16)
=>; 9x 24 = 3x 24 48
=>; 9x 24 = 3x 72
=>; 9x – 3x = 72 – 24 Þ 6x = 48
=>; x = 48/6 = 8
Required ratio 8 years ago,
= (x 8) : (9x 8)
= (8 8) : (9 × 8 8)
= 16 : 80 = 1 : 5

4. The ratio of the present ages of two boys is 3 : 4. After 3 years, the ratio of their ages is equal to will be 4 : 5. The ratio of their ages after 21 years will be?
a) 14:17 b) 12:13 c) 10:11 d) 11:12
Ans: c
Solution: Let the ages of boys be 3x and 4x years respectively.
According to the question,
After 3 years
(3x 3) / (4x 3) = 4/5
=>; 16x 12 = 15x 15
=>; 16x – 15x = 15 – 12
=>; x = 3
 Required ratio after 21 years
(3x 21) / (4x 21) = (3 × 3 21) / (4 × 3 21) = 9 21 / 12 21
= 30 / 33 = 10/11 = 10 : 11

To be continued…
M. Venkat
Director
MVK Publications
Dilsukhnagar
7671002120