A number $x$ is decreased by $m$ $%$ and some other number $y$ is increased by $m$ $%$ . If both the results are equal, find $m$ in terms of $x$ and $y$ . Also, find $m$ if $2 x = 3 y$

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

;

m = 20

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

;

m = 20

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

;

m = 10

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None of these

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Solution

The correct option is C $m = \frac{100 (x - y)}{x + y}$ ; $m = 20$
Let the number are $x$ and $y$
When $m %$ decreased $=$ $\frac{x \times m}{100}$
When $m %$ increased $=$ $\frac{y \times m}{100}$
Both are equal, then
$x - \frac{x m}{100} = y + \frac{y m}{100}$
$\Rightarrow x - y = \frac{x m}{100} + \frac{y m}{100}$
$\Rightarrow x - y = \frac{m}{100} (x + y)$
$\Rightarrow m = \frac{100 (x - y)}{x + y}$
Given, $2 x = 3 y$ , then $x = \frac{3 y}{2}$
Then $m = \frac{100 (x - y)}{x + y}$
So, $m =$ $\frac{100 (\frac{3 y}{2} - y)}{\frac{3 y}{2} + y}$
$\Rightarrow \frac{100 (3 y - 2 y)}{3 y + 2 y}$
$\Rightarrow \frac{100 y}{5 y} = 20$

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