Question

The ages 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.

Answer 1

Let the age of Ani and Biju be x and y respectively.

Then according to the question-

$x-y=3$..........(i)

Dharam is twice the age of Ani

Hence, age of Dharam $=2x$

Age of Cathy is half the age of Biju

Then age of Cathy $=\frac{y}{2}$

Then according to the question

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

$\Rightarrow 4x-y=60$......(ii)

Subtracting (ii) from (i)

$\Rightarrow x-y-4x+y=3-60$

$\Rightarrow -3x=-57$

$\Rightarrow x=\frac{-57}{-3}=19$

Substitute the vale of x in (i)

$\Rightarrow 19-y=3$

$\Rightarrow -y=-16$

$\Rightarrow y=16$

$\therefore$ Age of Ani $=19$ years and age of Biju $=16$ years.