# 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 age of Cathy and Dharam are differ by 30 years. Find the ages of Ani and Biju.

## Solution :

Let x and y be the ages of Ani and Biju respectively. Then,

According to Question,

x + y = $$\pm 3$$

Dharam’s age = 2x,  and  Cathy’s age = $$y\over 2$$

Clearly, Dharam is older than Cathy.

So, 2x – $$y\over 2$$ = 30

$$\implies$$  4x – y = 60

Thus, we have these two linear equations,

x – y = 3               …….(1)

4x – y = 60            ……….(2)

or   x – y = -3            ……..(3)

4x – y = 60          ……..(4)

On Subtracting equation (2) from (1), we get

-3x = -57      $$\implies$$    x = 19

Put the value of x = 19 in equation (1), we get

19 – y = 3   $$\implies$$   y = 16

Now, On Subtracting equation (3) from (4), we get

3x = 63     $$\implies$$    x = 21

Put the value of x = 21 in equation (3), we get

21 – y = – 3     $$\implies$$     y = 24

Hence, Ani’s age is 19 years and Biju’s is 16 years

or Ani’s age is 21 years and Biju’s age is 24 years