Question

Five years ago age of Ankita was thrice the age of Ajita. After $10$ years Ankita's age will be twice the age of Ajita. Find the present ages of Ankita and Ajita.

Answer 1

Let the present age of Ankita be $x$ years and that of Ajita be $y$ years.
Five year's ago
Age of Ankita $=(x-5)$ years and
Age of Ajita$=(y-5)$ years

According to the question, we have $x-5=3(y-5)$
or $x-3y=-10$ ..........(i)

After ten years,
Age of Ankita will be $=(x+10)$ years
and age of Ajita will be $=(y+10)$ years

According to the question, we have
$x+10=2(y+10)$
or $x-2y=10$ ............(ii)

Subtracting eq.(i) from eq.(ii), we get

$y=20$

Hence, $x-3\left(20\right)=-10$

$\therefore x=50$

Thus, the present age of Ankita is $50$ years and that of Ajita is $20$ years.