A student multiplied a number by 3/5 instead of 5/3 . What is the percentage error in the calculation?

Correct option is C

Given:

The student multiplied a number by 3/5 instead of 5/3.

Formula Used:

Percentage error = (Correct result - Incorrect result) / Correct result × 100

Solution:

Correct result =  $$x \times \frac{5}{3}$$​​

Incorrect result = $$x \times \frac{3}{5}$$​​

Percentage error = $$\frac{x \times \frac{5}{3} - x \times \frac{3}{5}}{x \times \frac{5}{3}} \times 100$$​​

Percentage error =  $$\frac{\frac{5x}{3} - \frac{3x}{5}}{\frac{5x}{3}} \times 100$$​​

Percentage error = $$\frac{\frac{25x - 9x}{15}}{\frac{5x}{3}} \times 100$$​​

Percentage error =  $$\frac{16x}{15} \times \frac{3}{5x} \times 100$$​​

Percentage error = $$\frac{16}{25} \times 100$$​​

Percentage error = 64%

Therefore, the percentage error in the calculation is 64%.