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.

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=y/2
Then according to the question
2x−y/2=30⇒4x−y=60. (ii)
Subtracting (ii) from (i)
⇒x−y−4x+y=3−60
⇒−3x=−57
⇒x=−57/−3=19
Substitute the vale of x in (i)
⇒19−y=3
⇒−y=−16
⇒y=16
∴Age of Ani=19years and age of Biju=16years.