Question

Two brothers have their age in the ratio of 2:3. After five years what will be the ratio of their ages. The sum of their ages after 5 years is 30.

(a) \(\frac{3}{4}\)

(b) \(\frac{4}{3}\)

(c) \(\frac{2}{3}\)

(d) \(\frac{3}{2}\)

This question was addressed to me in a national level competition.

I'm obligated to ask this question of Age/Money/Denomination of Currency Word Problems topic in chapter Linear Equations in One Variable of Mathematics – Class 8

Answer 1

Correct answer is (a) \(\frac{3}{4}\)

Explanation: Let the common ratio be x. The age of two brothers after five years would be (2x+5) years and (3x+5)years.

Therefore (2x+5)+(3x+5)=30

Therefore 2x+5+3x+5=30

Therefore 5x=20

Therefore x=4

Therefore the brothers age would be 10 years and 15 years respectively.

Now, after five years their ages would be 15 years and 20 years respectively.

The ratio of the brothers ages = \(\frac{15}{20} = \frac{3}{4}\).