Question

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be $160$. Find the present age of her sister.

• A. $12$ yrs
• B. $6$ yrs
• C. $8$ yrs
• D. $9$ yrs

Answer 1

The correct option is B $6$ yrs

Let the girl's age be $2x$, then the sister will be $x$ years

$4$ years hence,

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

$2x^2+12x-144=0$

$2x^2+24x-12x-144=0$

$2x(x+12)-12(x+12)=0$

$(x+12)(2x-12)=0$

$x=6$ or $-12$

Since speed can not be negative,$x=6$ years