Question

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.

Answer 1

Let the present ages of Tanvy and Divya be $$5x$$ years and $$7x$$ years respectively.

After 5 years, their ages will be $$(5x + 5)$$ and $$(7x + 5)$$. 

According to the problem: $$\frac{5x + 5}{7x + 5} = \frac{3}{4}$$ 

Cross-multiply: $$4(5x + 5) = 3(7x + 5)$$

$$20x + 20 = 21x + 15$$

$$21x - 20x = 20 - 15$$

$$\implies x = 5$$ 

Present ages:

Tanvy's present age = $$5 \times 5 = 25\text{ years}$$.

Divya's present age = $$7 \times 5 = 35\text{ years}$$.