Question

The difference between the ages of two brothers today is 4 years. Five years ago, the ratio of their ages was 5 : 7. Find the age of the younger brother.

Answer 1

Let the elder brother’s age be x years.
Then, the younger brother’s age will be (x − 4) years.
Five years ago elder brother’s age = (x − 5) years
And five years ago younger brother’ age = x − 4 − 5 = (x − 9) years
Ratio of their ages 5 years ago was 5:7.
Hence,$\frac{x-9}{x-5}=\frac{5}{7}$
⇒ 7(x − 9) = 5 (x − 5)
⇒ 7x − 63 = 5x − 25
⇒ 2x = 38
∴ x = 19
The elder brother’s age = x = 19 years
And the younger brother age = x − 4 = 19 − 4 = 15 years
∴ Age of younger brother = 15 years