A number is mistakenly multiplied by$\frac{7}{5}$ instead of being multiplied by $\frac{3}{2}$. What is the percentage change in the result due to this mistake?

$6\frac{2}{3}$%

Let number is = 10x

Wrongly multiplied by \(\frac{7}{5}\) . So , number we get =

= \(\frac{7}{5}\) × 10x = 14x

In actual it should be multiplied by \(\frac{3}{2}\) . So , desired number =

= \(\frac{3}{2}\) × 10x = 15x

Difference = 15x - 14x = 1x

Percentage error = \(\frac{1x}{15x}\)  × 100

= \(\frac{1}{3}\)  × 20

= 6\(\frac{2}{3}\)%