The current ages of 'Arjun' and 'Bhanu' are in the ratio of 3:2, respectively. 'Y' years ago, the age of 'Chetna' was 40% less than the age of 'Bhanu'. Five years from now, the age of 'Chetna' will be half the age of 'Arjun'. If five years ago, the ages of 'Arjun' and 'Bhanu' were in the ratio of 8:Y, respectively, then determine the current age of 'Chetna'. [Ages of 'Arjun', 'Bhanu', and 'Chetna' can only take integral values]

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