Question

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

Answer 1

Let the present ages of the younger sister be ‘a’. 

Given, girl is twice as old as her sister. 

Age of elder sister = 2a 

Also, four years ago, the product of their ages (in years) will be 160. 

⇒ (a + 4)(2a + 4) = 160 

⇒ 2a² + 12a + 16 – 160 = 0 

⇒ a² + 6a – 72 = 0 

⇒ a² + 12a – 6a – 72 = 0 

⇒ a(a + 12) – 6(a + 12) = 0 

⇒ (a – 6)(a + 12) = 0 

⇒ a = 6 years 

Age of sisters – 6 years and 12 years