Present ages of 'Ajay' and 'Bheem' are in ratio 5:8, respectively. Five years hence from now, Ajay's age will be 25% less than that of 'Charu'. If present age of 'Charu' is an integer and sum of present ages of 'Ajay' and 'Bheem' together is less than 110 years, then determine the maximum present age of 'Charu'.

ATQ, Let the Ajay, Bheem and Charu can be defined as 'A', 'B' and 'C' respectively. Then, the present ages of 'A' and 'B' be '5x' years and '8x' years. So, age of 'C' five years hence from now = (5x + 5) ÷ 0.75 Since, present age of 'C' is an integer, (x + 1) must be divisible by 3. (As 20 is not) So, possible values of 'x' = 2, 5, 8 and so on. At 'x' = 2, present age of 'C' = {20 X 3 ÷ 3} - 5 = 15 years And sum of ages of 'A' and 'B' = 5x + 8x = 13x = 13 X 2 = 26 years At 'x' = 5, present age of 'C' = {20 X 6 ÷ 3} - 5 = 35 years And sum of ages of 'A' and 'B' = 5x + 8x = 13x = 13 X 5 = 65 years At 'x' = 8, present age of 'C' = {20 X 9 ÷ 3} - 5 = 55 years And sum of ages of 'A' and 'B' = 5x + 8x = 13x = 13 X 8 = 104 years At 'x' = 11, present age of 'C' = {20 X 12 ÷ 3} - 5 = 75 years And sum of ages of 'A' and 'B' = 5x + 8x = 13x = 13 X 11 = 143 years Since, sum of ages of 'A' and 'B' must be less than 110, the maximum possible age of 'C' is attained at 'x' = 8. So, maximum present age of 'C' = 55 years