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.

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