Six years ago, the ratio of the ages of 'A' and 'B' was 3:5, respectively. However, eight years from now, the ratio of their ages will be 5:6. Determine the age of 'B' two years from now.

Let the ages of 'A' and 'B' six year ago from now be '3y' and '5y' years respectively. So, present ages of 'A' and 'B' will be (3y + 6) and (5y + 6) years respectively. ATQ: (3y + 6 + 8) :(5y + 6 + 8) = 5:6 Or, (3y + 14) :(5y + 14) = 5:6 Or, 6 X (3y + 14) = 5 X (5y + 14) Or, 18y + 84 = 25y + 70 Or, 7y = 14 So, 'y' = 2 So, present age of 'B' = 5 X 2 + 6 = 16 years So, age of 'B' 2 years hence from now = 16 + 2 = 18 years Let the ages of 'A' and 'B' six year ago from now be '3y' and '5y' years respectively. So, present ages of 'A' and 'B' will be (3y + 6) and (5y + 6) years respectively. ATQ: (3y + 6 + 8) :(5y + 6 + 8) = 5:6 Or, (3y + 14) :(5y + 14) = 5:6 Or, 6 X (3y + 14) = 5 X (5y + 14) Or, 18y + 84 = 25y + 70 Or, 7y = 14 So, 'y' = 2 So, present age of 'B' = 5 X 2 + 6 = 16 years So, age of 'B' 2 years hence from now = 16 + 2 = 18 years