Question

The number $x$ is decreased by $m\%$ and the number $y$ is increased by $(m+10)\%.$ Their ratio is $1:1$ after increase and decrease.
If $x:y=5:2;$ find the value of m.

Answer 1

When $x$ is decreased by $m$ %, new $x=x-\frac{mx}{100}$
And when $y$ is increased by $(m+10)$ %, new $y=y+\frac{(m+10)y}{100}$
Given, the results are equal
$x-\frac{mx}{100}=y+\frac{(m+10)y}{100}$
$=>100x-mx=100y+my+10y$
$=>100x-mx=110y+my$
$=>mx+my=100x-110y$
$=>m(x+y)=100x-110y$
$m=\frac{100x-110y}{x+y}$
When, $\frac{x}{y}=\frac{5}{2}$
$x=\frac{5y}{2}$
Putting value of $x$ in $m$
we get $m=\frac{100\left(\frac{5y}{2}\right)-110y}{\frac{5y}{2}+y}=\frac{500y-220y}{5y+2y}=\frac{280}{7}=40$