The age of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Given:

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju as twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years.

To do:

We have to find the ages of Ani and Biju.

Solution:

Let the ages of Ani and Biju be $x$ and $y$ years respectively.

This implies,

$x - y = 3$ ….(i)

Ani’s father Dharam’s age $= 2x$

Cathy’s age $= \frac{1}{2}y$

The ages of Cathy and Dharam differ by 30 years.

$\Rightarrow 2x - \frac{1}{2}y = 30$

$\frac{2(2x)-y}{2}=30$

$4x - y = 60$ ….(ii)

Subtracting equation (i) from equation (ii), we get,

$4x-y-(x-y)=60-3$

$4x-x-y+y=57$

$3x = 57$

$x = \frac{57}{3}$

$x=19$

Substituting $x=19$ in equation (i), we get,

$19-y=3$

$y=19-3$

$y=16$

Therefore, Anil’s age is 19 years and Biju’s age is 16 years .