Question

What percentage of 2 hours is 36 minutes?

Answer 1

Hint: In this question, we need to determine that 36 minutes is how much percentage of 2 hours. For this, we will convert the units in one form and then evaluate the percentage by following the relation between both the quantities.

Complete step-by-step answer:
One hour includes 60 minutes. Here, 2 hours is involved so, by the unitary method
$$\begin{gathered} \Rightarrow 1hr=60min \\ \Rightarrow 2hr=2\times 60min \\ \Rightarrow =120min \end{gathered}$$
Now, 100 times the ratio of first quantity and the second quantity results in the percentage of the first quantity with respect to the second quantity. Mathematically, $P_{ab}={\displaystyle \frac{a}{b}}\times 100\mathrm{\%}$ where, $P_{ab}$ is the percentage of ‘a’ with respect to ‘b’.
According to the question, we need to determine the percentage of 36 minutes with respect to 2 hours (or 120 minutes).
So, substitute a=36 minutes and b=120 minutes in the equation $P_{ab}={\displaystyle \frac{a}{b}}\times 100\mathrm{\%}$ to determine the percentage of 36 minutes with respect to 120 minutes.
$$\begin{gathered} \Rightarrow P_{ab}={\displaystyle \frac{a}{b}}\times 100\mathrm{\%} \\ ={\displaystyle \frac{36}{120}}\times 100\mathrm{\%} \\ ={\displaystyle \frac{3}{10}}\times 100\mathrm{\%} \\ =0.3\times 100\mathrm{\%} \\ =30\mathrm{\%} \end{gathered}$$
Hence, we can say that 36 minutes is 30% of 2 hours.

Note: Students must be careful while substituting the values for the numerator and the denominator. The numerator is the part for which we need to evaluate the percentage value while the denominator is the part with respect to which the percentage needs to be evaluated. Alternatively, we can also convert the minutes to hours and then follow the percentage relation to get the result. Here, 36 minutes will be equivalent to 3/5 hours. So, the percentage is
$$\begin{gathered} \Rightarrow P_{ab}={\displaystyle \frac{a}{b}}\times 100\mathrm{\%} \\ ={\displaystyle \frac{\left({\displaystyle \frac{3}{5}}\right)}{2}}\times 100\mathrm{\%} \\ ={\displaystyle \frac{3}{10}}\times 100\mathrm{\%} \\ =0.3\times 100\mathrm{\%} \\ =30\mathrm{\%} \end{gathered}$$