1. 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 age difference between Ani and Biju is 3 yrs. Either Biju is 3 years older than that of Ani or Ani is 3 years older than Biju. From both the cases we find out that Ani’s father’s age is 30 yrs more than that of Cathy’s age. Let the ages of Ani and Biju be A and B respectively. Therefore, the age of Dharam = 2 x A = 2A yrs. And the age of Biju sister Ann B/2 yrs By using the information that is given, Case (i) When Ani is older than that of Biju by 3 yrs then A – B = 3 – – – – – – – – (1) 2A−B/2 = 30 4A – B = 60 – – – – – – – – – – – (2) By subtracting the equations (1) and (2) we get, 3A = 60 – 3 = 57 A = 57/3 = 19 Therefore, the age of Ani = 19 yrs And the age of Biju is 19 – 3 = 16 yrs. Case (ii) When Biju is older than Ani, B – A = 3 – – – – – – – – – (1) 2A − B/2 = 30 4A – B = 60 – – – – – – – – – (2) Adding the equation (1) and (2) we get, 3A = 63 A = 21 Therefore, the age of Ani is 21 yrs And the age of Biju is 21 + 3 = 24 yrs.