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

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{number}}\,{\text{be}}\,x \cr & {\text{Then,}}\,{\text{error}} = \frac{5}{3}x - \frac{3}{5}x = \frac{{16}}{{15}}x. \cr & {\text{Error}}\% = \left( {\frac{{16x}}{{15}} \times \frac{3}{{5x}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 64\% \cr} $$