A student erroneously multiplied a number by $$\frac 25$$​ instead of $$\frac52.$$​ The percentage error in the calculation is:

Correct option is B

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Given:
A student erroneously multiplied a number by$$\frac 25$$​ instead of $$\frac 52$$​
Solution:
Let the number be x.
Ideally, he should have multiplied by x by $$\frac 52$$​
Hence Correct result was x × $$\frac 52= \frac {5x}2$$​​
By mistake he multiplied x by$$\frac 25$$​,
Hence the result with error = $$\frac{2x}5$$​​
Then, error = $$\frac {5x}{2} - \frac{2x}{5} = \frac {21 x}{10}$$​​
​$$\text{Error \%} = \left( \frac{\text{Error}}{\text{True Value}} \right) \times 100 = \left( \frac{\frac{21x}{10}}{\frac{5x}{2}} \right) \times 100 = 84\% \\\therefore \text{Percentage Error} = 84\%$$​​