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 years respectively.
Therefore, age of Ani’s father, Dharam = 2 × x = 2x years
And age of Biju’s sister Cathy = y / 2 years
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
3x = 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.
