Question

A girl is twice as old as her sister . four years hence, the product of their ages will be 160. find their present ages.

Answer 1

I hope that it's clear enough.

Answer 2

Answer:

6 years and 12 years

Step-by-step explanation:

Let the younger sister's present age be x ∴ elder sister's present age = 2x

4 years hence

Younger sister will be x + 4 years old and elder will be 2x + 4 years old

According to Question

( x + 4) ( 2x + 4) = 160

2x² + 4x + 8x + 16 = 160

2x² + 12x - 144 = 0 or

x² + 6x - 72 = 0 [both sides divided by 2]

Splitting middle term

x² + 12x - 6x - 72 = 0       [∵ 12×6 = 72 and 12 - 6 = 6]

Taking x common from first two terms and -6 from last two terms

x ( x + 12) - 6 (x + 12) = 0

(x + 12) ( x - 6) = 0

x + 12 = 0               x - 6 = 0

x = -12                    x = 6

∵ Age can not be negative, neglecting x = -12

∴ Present Age of younger sister (x) = 6 years

and present age of elder sister (2x) = 12 years