Question

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Their present ages are 6 years and 12 years.

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ Let present age of girl be $2x$.

$\Rightarrow$ Then, age of her sister be $x.$

According to the question,

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

$\Rightarrow$ $2x^2+8x+4x+16=160$

$\Rightarrow$ $2x^2+12x+16-160=0$

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

$\Rightarrow$ $2(x^2+6x-42)=0$

$\Rightarrow$ $x^2+6x-72=0$

$\Rightarrow$ $x^2+12x-6x-72=0$

$\Rightarrow$ $x(x+12)-6(x+12)=0$

$\Rightarrow$ $(x+12)(x-6)=0$

$\Rightarrow$ $x+12=0$ and $x-6=0$

$\therefore$ $x=-12$ and $x=6$

$\Rightarrow$ Age cannot be negative.

$\therefore$ $x=6$

$\Rightarrow$ $2x=2\times 6=12$

$\therefore$ The present ages of girls are $6years$ and $12years.$