Seven years ago, the ages (in years) of A and B were in the ratio 4 : 5 and 7 years hence, their ages will be in the ratio 5 : 6. What will be the ratio of their ages 5 years from now?

34 : 41

ATQ,

Let, 7 years ago ages of A and B were 4x and 5x respectively

Present age of A and B is 4x + 7 and 5x + 7

Given, 7 years hence ratio of their ages = \(\frac{4x + 7 + 7}{5x +7 + 7}\) =\(\frac{5}{6}\)

                                                         ⇒ 24x + 84 =25x + 70

                                                            x = 14

Ratio of their ages 5 years from now = \(\frac{4×14 + 7 + 5}{5×14 + 7 + 5}\)

                                                      = \(\frac{68}{82}\)

Ratio of age of A and B, after 5 years = 34:41