Question

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

Answer 1

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.

Complete step-by-step answer:
We have been given that a student erroneously multiplied a number by $\dfrac{2}{5}$ instead of $\dfrac{5}{2}$.
So, let the number with which they were to be multiplied by x.
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\% $
Further solving we get,
$ \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\% $
Hence, the percentage error in the calculation is 84%.

Note: Whenever we face such types of problems the crux point to remember is that we need to have a good grasp over the concept and the formula to calculate errors. In these types of questions, we should always assume a number and then proceed as this makes solving the questions much easier and gets us on the right track to reach the answer.