Question

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

Answer 1

Let the number be x.

Then, ideally he should have multiplied by x by $\frac{5}{3}$ . Hence Correct result was $x\times \frac{5}{3}=\frac{5x}{3}$

By mistake he multiplied x by $\frac{3}{5}$ . Hence the result with error $=\frac{3x}{5}$

Then, error $=\frac{5x}{3}-\frac{3x}{5}=\frac{16x}{15}$

Error % $=\left(\frac{error}{truevalue}\right)\times 100$ $=\left[\frac{\left(\frac{16}{15}\right)x}{\left(\frac{5}{3}\right)x}\right]\times 100=64$ %