The ages of Tanvy and Divya are in the ratio 5 : 7. Five years hence, their ages will be in the ratio 3 : 4. Find their present ages.

Given,

The ages of Tanvy and Divya are in the ratio 5 : 7.

Let the present age of Tanvy be 5x and the present age of Divya be 7x.

Five years from now :

Tanvy's age will be 5x + 5.

Divya's age will be 7x + 5.

Given,

The ratio of their ages in five years will be 3 : 4.

$\Rightarrow \dfrac{5x + 5}{7x + 5} = \dfrac{3}{4}$

⇒ 4(5x + 5) = 3(7x + 5)

⇒ 20x + 20 = 21x + 15

⇒ 21x - 20x = 20 - 15

⇒ x = 20 - 15

⇒ x = 5.

Tanvy's present age = 5x = 5(5) = 25 years.

Divya's present age = 7x = 7(5) = 35 years.

Hence, present age of Tnavy and Divya are 25 years and 35 years respectively.