The current ages of 'Arjun' and 'Bhanu' are in the ratio

Solution

ATQ, Let the present ages of 'Arjun' and 'Bhanu' be '3a' years and '2a' years, respectively. So, present age of 'Chetna' = [{(3a + 5) /2} - 5] years ATQ; (2a - Y) × (6/10) = [{(3a + 5) /2} - 5] - Y Or, 12a - 6Y = 15a - 25 - 10Y So, 4Y = 3a - 25 ......... (I) Also, {(3a - 5) /(2a - 5) } = (8/Y) Or, Y × (3a - 5) = 8 × (2a - 5) So, Y = {(16a - 40) /(3a - 5) } On substituting the value of 'Y' in equation (II) , we have; 4 × {(16a - 40) /(3a - 5) } = 3a - 25 Or, 64a - 160 = (3a - 25) (3a - 5) Or, 64a - 160 = 9a²- 15a - 75a + 125 Or, 9a²- 154a + 285 = 0 Or, 9a²- 135a - 19a + 285 = 0 Or, 9a(a - 15) - 19(a - 15) = 0 Or, (9a - 19) (a - 15) = 0 So, a = 15 or a = (19/9) Since, age has to be an integer, a = 15 So, 4Y = 3 × 15 - 25 Or, 4Y = 20 So, Y = 5 So, present age of 'Chetna' = {(3a + 5) /2} - 5 = {(15 × 3) + 5) } ÷ 2 = 20 years = '4Y' years