Question

A student multiplied a number by $\frac{3}{5}$ instead of $\frac{5}{3}$. What is the percentage error in the calculation?

• A. $60$%
• B. $64$%
• C. $72$%
• D. $78$%

Answer 1

Answer: (B)

$64$%

Let the number be $x$.

Then, percentage error $=\left(\begin{array}{c}\frac{\frac{5}{3}x-\frac{3}{5}x}{\frac{5}{3}x}\end{array}\right)\times 100\%=\frac{\frac{25x-9x}{15}}{\frac{5x}{3}}\times 100\%$
$=\frac{16x}{15}\times \frac{3}{5x}\times 100\%=64\%$.