The ratio of ages of A and B, four years ago, was 4 : 5.  Eight years from now, the ratio of the ages of A and B will be 11 : 13.  What is the sum of their present age?

80

4 years ago ⇒ A : B = 4 : 5

⇒ \(\frac{4x + 12}{5x + 12}\) = \(\frac{11}{13}\)

⇒ 52x + 156 = 55x + 132

⇒ 24 = 3x

⇒ x = 8

4 years ago age of A and B = (4 x 8), (5 x 8) = 32, 40

Now, Present age of A and B = (32 + 4), (40 + 4) = 36, 44

Sum = 36 + 44 = 80 years