Question

The difference between the ages of two brothers is 10 years, and 15 years ago their ages were in the ratio 2:1. Find the ratio of their ages 15 years hence.

Answer 1

Given, The difference between the ages of two brothers is 10 years.
So, let their ages be x and (x - 10) years respectively.
Their ages 15 years ago are,
(x - 15) and (x - 25) respectively.
Also, given 15 years ago their were in the ratio 2 : 1.
As per given conditions,

`((x - 15))/((x - 25)) = (2)/(1)`
⇒ x - 15 = 2x - 50
⇒ x = 50 - 15 = 35 years.
Thus, their present ages are x = 35years and 20 years respectively.
Also, their ages 15 years hence are,
(x + 15) and x + 5 respectively = 50 and 40 years.
Thus, the ratio of their ages 15 years hence

`((x + 15))/((x) = (50)/(40) = (5)/(4)`.