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.

Explanation

Let the present age of her sister be x years.
Then, girl's present age =2x years.
Product of their ages 4 years hence `=(x+4)(2x+4).`
`:." "(x+4)(2x+4)=160`
`implies" "2x^(2)+12x-144=0impliesx^(2)+6x-72=0`
`implies" "x^(2)+12x-6x-72=0impliesx(x+12)-6(x+12)=0`
`implies" "(x+12)(x-6)=0impliesx+12=0" or "x-6=0`
`implies" "x=-12" or "x=6`
`implies" "x=6" "[because" the age cannot be negative"]`
`:." "sister's present age = 6 years and girl's present age = 12 years."`