5 years ago from now, the ratio of age of 'A' and 'B' was 9:5, respectively and 5 years hence from now, the ratio of their ages will become 11:7. Find the sum of their present ages.

5 years ago from now, let the ages of 'A' and 'B' be '9x' years and '5x' years, respectively. Therefore, 5 years hence from now, age of 'A' = (9x + 5 + 5) = (9x + 10) years ATQ, (9x + 10)/(5x + 10) = 11/7 Or, 63x + 70 = 55x + 110 Or, 8x = 40 So, 'x' = 5 So, age of 'A', 5 years ago from now = 9x = 9 X 5 = 45 years And, age of 'B', 5 years ago from now = 5x = 5 X 5 = 25 years So, Present age of 'A' = 45 + 5 = 50 years And, Present age of 'B' = 25 + 5 = 30 years Required sum = 50 + 30 = 80 years Alternate Solution Ratio of ages of 'A' and 'B' 5 years ago from now = 9:5 And, Ratio of ages of 'A' and 'B' 5 years hence from now = 11:7 Since, the difference between age of 'A', 5 years ago and 5 years hence from now is 10 years Therefore, (11 - 9) = 2 units = 10 years