#### 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

#### Solution

The difference between the ages of Biju and Ani is 3 years. Either Biju is 3 years older than Ani or Ani is 3 years older than Biju. However, it is obvious that in both cases, Ani’s father’s age will be 30 years more than that of Cathy’s age.

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

Therefore, age of Ani’s father, Dharam = 2 × x = 2x years

And age of Biju’s sister Cathy = `y/2` year

By using the information given in the question,

**Case (I) **When Ani is older than Biju by 3 years,

x − y = 3 (i)

`2x -y/2 = 30`

4x − y = 60 (ii)

Subtracting (*i*) from (*ii*), we obtain

3*x* = 60 − 3 = 57

`x = 57/3 =19`

Therefore, age of Ani = 19 years And age of Biju = 19 − 3 = 16 years

**Case (II) **When Biju is older than Ani,

y − x = 3 (i)

`2x - y/2 = 30`

*4x − y = 60 (ii)*

Adding (i) and (ii), we obtain

3x = 63

x = 21

Therefore, age of Ani = 21 years And age of Biju = 21 + 3 = 24 years