Question

The number x is decreased by m % and the number y is increased by (m = 10)% . Find m in terms of x and y.
If x : y = 5 : 2; find the value of m.

Answer 1

m% of x$=x\times \frac{m}{100}=\frac{xm}{100}$

when x is decreased m% $=x-\frac{xm}{100}$ ....(1)

m% of y $=y\times \frac{m}{100}=\frac{ym}{100}$

when y is increased m% $=y+\frac{ym}{100}$ ....(2)

Both (1) and (2) are equal.

$\Rightarrow x-\frac{xm}{100}=y+\frac{ym}{100}$

$\Rightarrow x-y=\frac{ym}{100}+\frac{xm}{100}$

$\Rightarrow x-y=\frac{m}{100}(x+y)$

$\Rightarrow \frac{100x-100y}{x+y}=m$

$\Rightarrow \frac{\frac{100x-100y}{y}}{\frac{x+y}{y}}=m$

$\Rightarrow \frac{100\frac{x}{y}-100}{\frac{x}{y}+1}=m$

$\Rightarrow \frac{100\times \frac{5}{2}-100}{\frac{5}{2}+1}=m$ [$\because Given\frac{x}{y}=\frac{5}{2}$]

$\Rightarrow \frac{150}{7}\times 2=m$

$\Rightarrow m=42.857$