Question

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

Answer 1

Let the real number be x

$\Rightarrow$ correct answer = $\frac{5x}{2}$ (Given)

Wrong answer = $\frac{2x}{5}$ (Given)

Error = correct answer - wrong answer

$=\frac{5x}{2}-\frac{2x}{5}=\frac{25x-4x}{10}=\frac{21x}{10}$

% error = $\frac{error}{correctanswer}\times 100$%

$=\frac{\frac{21x}{10}}{\frac{5x}{2}}\times 100=\frac{21x}{10}\times \frac{2}{5x}\times 100$

$=84$%