Question

A period of 4 hours 30 minutes makes up what percent of a day?

Answer 1

Hint: We know that there are 60 minutes in an hour. Let us assume the number of minutes in a day is equal to x. So, we have to find the number of minutes in a day. Let us assume the number of minutes in 4 hours 30 minutes is equal to y. Now we have to find the ratio of y and x. Now we have to find the percent of 4 hours 30 minutes in a day.

Complete step by step solution:
We know that there are 60 minutes in an hour.
Number of hours in a day = 24 hours
Let the number of minutes in a day be x.
\[x=(24\times 60)\]
\[\Rightarrow x=\text{ 1440}...\text{(1)}\]
In the question, we are given a period of 4 hours 30 minutes.
Number of minutes in 4 hours \[=(4\times 60)=240\]
Let the number of minutes in 4 hours 30 minutes be y.
\[\begin{align}
  & y=240+30 \\
 & \Rightarrow y=270.....(2) \\
\end{align}\]
Now we have to find the fraction of 4 hours 30 minutes in a day. So, we have to find the ratio of y and x.
So, from equation (1) and equation (2) we get
\[\begin{align}
  & \Rightarrow \dfrac{y}{x}=\dfrac{270}{1440} \\
 & \Rightarrow \dfrac{y}{x}=\dfrac{3}{16}.....(3) \\
\end{align}\]
So, from equation (3) we get the ratio of y and x is equal to \[\dfrac{3}{16}\].
Let the percent of 4 hours 30 minutes in a day is equal to p.
\[\begin{align}
  & \Rightarrow p=\left( \dfrac{3}{16}\times 100 \right)\% \\
 & \Rightarrow p=18.75\% \\
\end{align}\]
So, the percent of 4 hours 30 minutes in a day is equal to \[18.75\%\].

Note: Students may have a misconception that to calculate the percent of 4 hours 30 minutes in a day, we can take the ratio of x and y (or) we can take the ratio of y and x. But we should take the ratio of y and x to calculate the percentage. Because the maximum value of percentage is equal to 100 %. If we consider the ratio of x and y to calculate the percentage, the obtained percentage will be greater than 100 % which is not possible in general conditions. So, we should consider the ratio of y and x to calculate the percentage.