Question

Two numbers are in the ratio $5:6$. If $8$ is subtracted from each of the numbers, the ratio becomes $4:5$. Find the numbers.

Answer 1

Let numbers are $5x$ and $6x$

$\frac{(5x-8)}{(6x-8)}=\frac{4}{5}$

$\Rightarrow 5(5x-8)=4(6x-8)$

$\Rightarrow 25x-40=24x-32$

$\Rightarrow 25x-24x=40-32$

$\Rightarrow x=8$

Two numbers are

$5\times 8=40$ and $6\times 8=48$