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# A student erroneously multiplied a number by $\dfrac{2}{5}$ instead of $\dfrac{5}{2}$. What is the percentage error in the calculation?

Last updated date: 14th Jul 2024
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Hint: In this question we have to find the percentage error in the calculation of the multiplications done by the student. Here we will assume the number with which the given number is multiplied. Then using the formula to calculate the error we will proceed with the question.

We have been given that a student erroneously multiplied a number by $\dfrac{2}{5}$ instead of $\dfrac{5}{2}$.
Then, the wrong number we got is $\dfrac{2}{5}x$ and the right number is $\dfrac{5}{2}x$.
So, using the formula for calculating error, that is ${\text{Error% }} = \dfrac{{{\text{Right Answer - Wrong Answer}}}}{{{\text{Right Answer}}}} \times 100\%$
$\Rightarrow {\text{Error% }} = \dfrac{{\dfrac{5}{2}x - \dfrac{2}{5}x}}{{\dfrac{5}{2}x}} \times 100\%$
$\Rightarrow {\text{Error% }} = \dfrac{{\dfrac{{25 - 4}}{{10}}x}}{{\dfrac{5}{2}x}}$
$\Rightarrow {\text{Error% }} = \dfrac{{\dfrac{{21}}{{10}}}}{{\dfrac{5}{2}}} = \dfrac{{21 \times 2}}{{5 \times 10}}$
$\Rightarrow {\text{Error% }} = \dfrac{{21}}{{25}} \times 100 = 84\%$