Question

The ratio of two numbers is $9:5$. If $9$ is added to the greater number and $5$ is subtracted from the smaller number, the greater number becomes thrice the smaller one. Find the numbers.

Answer 1

Present ratio $=9:5$.

Let $x$ be the common factor.

Thus, actual values are $9x$ and $5x$.
Hence $\frac{9x+9}{5x-5}=\frac{3}{1}$

$9x+9=15x-15$

$x=4$.

Thus, $x=4$

numbers are $9\times 4=36$ and $5\times 4=20$.