The ages of A and B are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

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

According to the question:

Ten years hence, the ratio of their ages will be 9 : 7.

$⇒ \dfrac{\text{Present age of A + 10}}{\text{Present age of B + 10}} = \dfrac{9}{7}\\[1em] ⇒ \dfrac{7x + 10}{5x + 10} = \dfrac{9}{7}\\[1em]$

By cross multiplying, we get :

⇒ 7(7x + 10) = 9(5x + 10)

⇒ 49x + 70 = 45x + 90

⇒ 49x - 45x = 90 - 70

⇒ 4x = 20

⇒ x = $\dfrac{20}{4}$

⇒ x = 5

So, present age of A = 7x

= 7 x 5

= 35 years

And, present age of B = 5x

= 5 x 5

= 25 years

Hence, the present ages of A and B are 35 years and 25 years, respectively.