What percentage is $2\mathrm{minutes}24\mathrm{seconds}$ of an hour?

Convert fraction into percentage.

First, we have to convert $2\mathrm{minutes}24\mathrm{seconds}$ into minutes.

$$\begin{gathered} 2\mathrm{minutes}24\mathrm{seconds}=\left(2+\frac{24}{60}\right)\mathrm{minutes}\left[\because 1\mathrm{minute}=60\mathrm{seconds}\right] \\ \Rightarrow =2+\frac{2}{5} \\ \Rightarrow =\frac{12}{5}\mathrm{minutes} \end{gathered}$$

Let us consider that $x\%$ of an hour is equal to $2\mathrm{minutes}24\mathrm{seconds}$.

$$\begin{gathered} \therefore x\%\mathrm{of}\mathrm{an}\mathrm{hour}=\frac{12}{5}\mathrm{minutes} \\ \Rightarrow \frac{x}{100}\times 60=\frac{12}{5}\left[\because 1\mathrm{hour}=60\mathrm{minutes}\right] \\ \Rightarrow x=\frac{12}{5}\times \frac{100}{60} \\ \Rightarrow x=\frac{100}{25} \\ \Rightarrow x=4 \end{gathered}$$

Hence, $4\%$ of an hour is equal to $2\mathrm{minutes}24\mathrm{seconds}$.