Six years ago the ratio of the ages of Preeti and Ruchi was 6: 5. After four years the ratio of their ages will be 11: 10. What is Ruchi's present age?

16 yr

Six years ago, the ratio of the ages of Preeti and Ruchi was $6:5$. Let's assume their ages six years ago were $6x$ and $5x$.

Therefore, their present ages are:

• Preeti's present age = $6x + 6$
• Ruchi's present age = $5x + 6$

Four years from now, their ages will be:

• Preeti's age after 4 years = $(6x + 6) + 4 = 6x + 10$
• Ruchi's age after 4 years = $(5x + 6) + 4 = 5x + 10$

The problem states that this future ratio will be $11:10$:

$\frac{6x + 10}{5x + 10} = \frac{11}{10}$

$10(6x + 10) = 11(5x + 10)$

$60x + 100 = 55x + 110$

$60x - 55x = 110 - 100$

$5x = 10$

$x = 2$

Substitute $x = 2$ back into Ruchi's present age expression ($5x + 6$):

$\text{Ruchi's present age} = 5(2) + 6 = 10 + 6 = 16\text{ years}$