The present ages of 'A' and 'B' are in the ratio of 5:8.

Solution

Let the present ages of 'A' and 'B' be '5x' years and '8x' years, respectively. So, age of 'C' five years hence from now = (5x + 5) ÷ 0.75 = 5(x + 1)/(3/4) = 20(x + 1)/3 So,present age of 'C' = 20(x + 1)/3 - 5 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