Question

The ages of A and B are in the ratio 5:7.Eight years ago,were in the 7:13.Find thier present ages

Answer 1

Let the present ages of A and B be 5x and 7x years respectively.

A'S age 8 years ago = (5x - 8) years.

B's age 8 years ago = (7x - 8) years.

∴ $\frac{5x - 8}{7x - 8} = \frac{7}{13}$  ⇒ 13(5x - 8) = 7(7x - 8)

                                                                              ⇒ 65x - 104 = 49x - 56

                                                                              ⇒ 65x - 49x = 104 - 56

                                                                              ⇒ 16x = 48

                                                                              ⇒ x = $\frac{48}{16} = 3$

∴ A's present age = 5x years = ( 5 × 3) years = 15 years.

  B's present age = 7x years = (7 × 3) years = 21 years.