Question : A man multiplied a number by $\frac{8}{5}$ instead of $\frac{5}{8}$, what is the percentage error in the calculation?
Option 1: 124%
Option 2: 162%
Option 3: 156%
Option 4: 100%
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Correct Answer: 156%
Solution :
Let the original number be $x$.
Correct result $=x× \frac{5}{8}$
present result $=x× \frac{8}{5}$
Difference $=\frac{8x}{5}-\frac{5x}{8}=\frac{39x}{40}$
$\therefore$ Percentage Error $=\frac{\frac{39x}{40}}{\frac{5x}{8}}×100=\frac{39x}{40}×\frac{8}{5x}×100=156\%$
Hence, the correct answer is 156%.
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