Question

What percentage of a day is $6\mathrm{hours}$ and $45\mathrm{minutes}$?

Answer 1

Convert fraction into percentage.

First, we have to convert $6\mathrm{hours}$ and $45\mathrm{minutes}$ into hours.

$$\begin{gathered} 6\mathrm{hours}45\mathrm{minutes}=\left(6+\frac{45}{60}\right)\mathrm{hours}\left[\because 1\mathrm{hour}=60\mathrm{minutes}\right] \\ \Rightarrow =6+\frac{3}{4} \\ \Rightarrow =\frac{27}{4}\mathrm{hours} \end{gathered}$$

Let us consider that $x\%$ of a day is equal to $6\mathrm{hours}$ and $45\mathrm{minutes}$

$$\begin{gathered} \therefore x\%\mathrm{of}\mathrm{a}\mathrm{day}=\frac{27}{4}\mathrm{hours} \\ \Rightarrow \frac{x}{100}\times 24=\frac{27}{4}\left[\because 1\mathrm{day}=24\mathrm{hours}\right] \\ \Rightarrow x=\frac{27}{4}\times \frac{100}{24} \\ \Rightarrow x=\frac{2700}{96} \\ \Rightarrow x=28.125 \end{gathered}$$

Hence, $28.125\%$ of a day is equal to $6\mathrm{hours}$ and $45\mathrm{minutes}$