Percentage | Arithmetic aptitude | Discussion Page

When a number is first increased by 10% and then is reduced by 10%, then the number

A) Decreases by 1%

B) Does not change

C) Increases by 1%

D) Cannot be determined

Option A

Let the number be = x

The no. is increased by 10% then the new no. $= x + \left(\frac{x}{10}\right)$ $= \left(\frac{11x}{10} \right)$

Now, the no. is decrease by 10%,

then the new no. $= \left(\frac{11x}{10} \right) - \left(\frac{11x}{100}\right)$ $= \frac{( 99x )}{ 100}$.

$\therefore$ Decrease in new no. $= x - \left(\frac{99x}{100} \right)$ $= \left(\frac{x}{100} \right)$

$\therefore$ % Decrease $= \left(\frac{x}{( 100 \times x )}\right) \times 100$ $= 1$%

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