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.

To find: Present ages

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

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

⇒ 2a² + 12a – 144 = 0

⇒ a² + 6a – 72 = 0

Split the middle term.

⇒ a² + 12a – 6a – 72 = 0

⇒ a (a + 12) – 6(a + 12) = 0

⇒ (a – 6) (a + 12) = 0

⇒ a = 6 and a =-12

As age cannot be negative,

⇒ a = 6 years

So 2a = 2(6) = 12 years

Hence age of sisters is 6 years and 12 years.