Ratio of ages of A and B, after 10 years will be 9:5, respectively. Present average age of A, B and C is 22 years. If present age of C is 50% more than age of A 6 years ago, then find the ratio of present ages of B and C respectively.

ATQ, ATQ, Let ages of A and B, after 10 years be 9x years and 5x years, respectively. Present age of A = 9x − 10 years Present age of B = 5x − 10 years Present age of C = 22 × 3 − [(9x − 10) + (5x − 10)] = 66 − (14x − 20) = 86 − 14x years According to the question, Present age of C is 50% more than age of A 6 years ago Age of A, 6 years ago = 9x − 10 − 6 = 9x − 16 So, 1.5 × (9x − 16) = 86 − 14x Or, 13.5x − 24 = 86 − 14x Or, 13.5x + 14x = 86 + 24 Or, 27.5x = 110 Or, x = 4 Present age of B = 5 × 4 − 10 = 20 − 10 = 10 years Present age of C = 86 − 14 × 4 = 86 − 56 = 30 years Desired Ratio (B : C) = 10 : 30 = 1 : 3