A student multiplied a number by $$\frac 27$$​ instead of $$\frac 57$$​. What is the percentage of error?

Correct option is B

Given:
A student multiplied a number by$$\frac 27$$​instead of $$\frac 57$$​.
Solution:
Let the number be x

.$$\text{Actual Product} = \frac{5}{7} \times x = \frac{5x}{7} \\\ \\\text{Wrong Product} = \frac{2}{7} \times x = \frac{2x}{7} \\\ \\\text{Percentage Error} = \left(\frac{\text{Actual Product} - \text{Wrong Product}}{\text{Actual Product}}\right) \times 100 \\\ \\= \left(\frac{\frac{5x}{7} - \frac{2x}{7}}{\frac{5x}{7}}\right) \times 100 = \frac{3}{5} \times 100=60\%$$
Alternate Solution:
​Let the number = 7
Actual product = $$\frac 57$$​ × 7 = 5

Wrong product = $$\frac 27$$​ × 7 = 2
Percentage Error = $$\frac{5 - 2}{5} \times 100 = \frac{3}{5} \times 100 = 60\%$$​​