A student multiplied a number by $frac{4}{5}$ instead of $frac{5}{4}$. What is the percentage error in the calculation?

Correct product $=frac{5 x}{4}$ where number = x Incorrect product $=frac{4 x}{5}$ Error $=frac{5 x}{4}-frac{4 x}{5}=frac{25 x-16}{20}=frac{9 x}{20}$ $herefore$ Error per cent $frac{frac{9 x}{20}}{frac{5 x}{4}} imes 100$ $=frac{9 x}{20} imes frac{4}{5 x} imes 100=36 \%$

Alternative :

LCM of 4 & 5 = 20

Correct product $=frac{5}{4} imes 20=25$

Incorrect product $=frac{4}{5} imes 20=16$

Percent erorr $=frac{25-16}{25} imes 100=36$ per cent