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.

(A-D) Let the age of Ani be $x$ years and the age of Biju be $y$ years.
Given that the difference between their ages is $3\, years,$ we have two cases:
Case $I$: $x - y = 3$ or Case $II$: $y - x = 3$.
Ani's father Dharam's age $= 2x$ years.
Biju's sister Cathy's age $= y/2$ years.
The difference between the ages of Dharam and Cathy is $30\, years,$ so $2x - y/2 = 30,$ which simplifies to $4x - y = 60$.
Case $I$: $x - y = 3$ and $4x - y = 60$.
Subtracting the first from the second: $(4x - y) - (x - y) = 60 - 3 \implies 3x = 57 \implies x = 19$.
Then $y = 19 - 3 = 16$.
Case $II$: $y - x = 3 \implies y = x + 3$.
Substituting into $4x - y = 60$: $4x - (x + 3) = 60 \implies 3x = 63 \implies x = 21$.
Then $y = 21 + 3 = 24$.
Thus,the ages of Ani and Biju are either $(19, 16)$ years or $(21, 24)$ years.