10 years ago, the ratio of the ages of Ramesh and Rajiv was 1:3. Now, after 5 years from now, this ratio will become 2:3. What is the ratio of their ages at present?

Explanation

Let the present ages of Ramesh and Rajiv be $x$ and $y$ respectively. According to the question $$\frac{x - 10}{y - 10} = \frac{1}{3}$$ $$3x - 30 = y - 10$$ $$3x - y = 20 \dots\dots\dots\dots(i)$$ and $$\frac{x + 5}{y + 5} = \frac{2}{3}$$ $$3x + 15 = 2y + 10$$ $$3x - 2y = -5 \dots\dots\dots\dots(ii)$$ From equation (i) and (ii) - $x = 15, y = 25$ Now $$\frac{x}{y} = \frac{15}{25} = \frac{3}{5}$$ $\Rightarrow x : y = 3 : 5$ Therefore, the ratio of the present ages of Ramesh and Rajiv is 3 : 5.