Question

The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharma is twice as old as Ani and Biju as twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Answer 1

Let the present ages of Ani, Biju, Dharam and Cathy be x, y, z and t years respectively.

The ages of Ani and Biju differ by 3 years. Thus, we have

Dharam is twice as old as Ani. Thus, we have

Biju is twice as old as Cathy. Thus, we have

The ages of Cathy and Dharam differ by 30 years. Clearly, Dharam is older than Cathy. Thus, we have

So, we have two systems of simultaneous equations

(i)

(ii)

Here x, y, z and t are unknowns. We have to find the value of x and y.

(i) By using the third equation, the first equation becomes

From the fourth equation, we have

Hence, we have

Using the second equation, we have

From the first equation, we have

Hence, the age of Ani isyears and the age of Biju isyears.

(ii) By using the third equation, the first equation becomes

From the fourth equation, we have

Hence, we have

Using the second equation, we have

From the first equation, we have

Hence, the age of Ani isyears and the age of Biju isyears.

Note that there are two possibilities.