Question

The ages of two brothers are 10 years and 14 years. In how many years time will the product of their ages be 285?

Answer 1

Let the required time be x years.

Younger brother’s age = 10 + x

Elder brother’s age = 14 + x

Given that the product of their ages will be 285:

(10 + x) (14 + x) = 285

x² + 24x + 140 = 285

x² + 24x − 145 = 0

(x + 29) (x − 5) = 0

x = −29 or x = 5

Reject the negative value.

The product of their ages will be 285 after 5​ years.