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 age of the girl in years ` = 2x`
Then, age of her sister in years ` = x`
We are given,
`(x+4)**(2x+4) = 160`
`=>2x^2+12x+16 = 160`
`=>2x^2+12x-144 = 0`
`=>x^2+6x-72 = 0`
`=>x^2+12x-6x-72 = 0`
`=>(x+12)(x-6) = 0`
`x = -12 and x = 6`
But, age can not be negative.
`:. x = 6`
`:.` Age of girl ` = 2**6 = 12` years
Age of her sister `= 6 ` years