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.

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

Age of Dharam = 2x years and Age of Cathy = \({{y}\over{2}}\) years

Case 1 : Ani's age is greater than Biju's age

According to question, x – y = 3… (1)
And \( 2x - {{y}\over{2}} = 30\)
\(4x – y = 60\)… (2)

Subtracting (1) from (2),:
\(3x = 60 – 3 = 57\)

x = Age of Ani = 19 years

Age of Biju = 19 – 3 = 16 years

Case 2 : Ani's age is less than Biju's age

Thus, \(y – x = 3\)… (3)
And \( 2x - {{y}\over{2}} = 30\)
\(4x – y = 60\)… (4)

Adding (3) and (4), we obtain:
3x = 63
x = 21

Age of Ani = 21 years
Age of Biju = 21 + 3 = 24 years