A student multiplied a number by $\frac{4}{5}$ instead of $\frac{5}{4}$ . What is the percentage error ?

30

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36

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40

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39

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Solution

The correct option is D $36$ %
Let the Number be $x$
Number becomes $\frac{4}{5} x$
If multiplied by $\frac{5}{4} x$
Error $= \frac{5}{4} x - \frac{4}{5} x$
$= \frac{9}{20} x$
Error percentage $= \frac{9 x \times 4}{20 \times 5 x} \times 100 = 36$ %

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