Question

You spend $7\dfrac{1}{2}$ hours out of $24$ hours at school. What percentage of a day is this?

Answer 1

Hint: In the question we have to find the percentage of a day if you have spent $7\dfrac{1}{2}$ hours out of $24$ hours at school. For this we will first understand the meaning of percentage then we will learn the percentage formula. Then we will substitute our given values in the percentage formula to get our required answer.

Complete step by step answer:
Percentage:
Percentage is a fraction of a ratio in which total value is$100$.
We represent the percentage using the $\%$symbol.
Formula for percentage is
Percentage $=\dfrac{\text{given value}}{\text{total value}}\times 100\%$
Now we will understand the meaning of percentage using an example
Suppose your teacher told you that you have got $80\%$ in your unit test
This means that out of total $100$ marks you got $80$ marks
Let us consider another example.
Example: find $20\%$ of $80$ .
We can solve it as
$\dfrac{20}{100}\times 80$
Now we will solve this
$\begin{align}
  & \dfrac{1600}{100} \\
 & \Rightarrow 16 \\
\end{align}$
$\therefore 16$ Is our required answer.
We can also calculate percentage increase or percentage decrease.
Formula for percentage increase or percentage decrease is
Percentage $=\dfrac{\text{final value - initial value}}{\text{initial value}}\times 100$
Where the initial value is our original value which will be changed further into the final value.
Now we will proceed to our question
In the question we have to find the percentage of a day if you have spent $7\dfrac{1}{2}$ hours out of $24$ hours at school.
Given time that you have spent in school $=7\dfrac{1}{2}$ hours
As we know, we can change mixed fraction in improper fraction
$\begin{align}
  & 7\dfrac{1}{2}=\dfrac{15}{2} \\
 & \\
\end{align}$
So,
We can also write it as
Given time that you have spent in school $=\dfrac{15}{2}$ hours
Total no. of hours in a day $=24$
Now formula for percentage is
Percentage $=\dfrac{\text{given value}}{\text{total value}}\times 100\%$
So according to question,
Our given value is $7\dfrac{1}{2}$ hours
And
Total value is $24$ hours.
We will substitute these values in percentage formula
Percentage $=\dfrac{7\dfrac{1}{2}}{24}\times 100\%$
As we have known that we can write $7\dfrac{1}{2}$ as $\dfrac{15}{2}$
So,
Percentage $=\dfrac{\dfrac{15}{2}}{24}\times 100\%$
We can write it as
Percentage $=\dfrac{15}{24\times 2}\times 100\%$
In simpler form
Percentage $=\dfrac{15}{48}\times 100\%$
$\Rightarrow \dfrac{1500}{48}\%$
Now we will solve this fraction
$\dfrac{1500}{48}\%=31.25\%$
$\therefore 31.25\%$Is our required answer.
You have spent $31.25\%$ of a day in school.

Note:
 In this question we have learnt about percentage and its formula. We can see its application in our day to day daily life. In shopping mall we have commonly observed that they offer various discounts like $50\%,20\%$ and so on. The amount we will pay is calculated using percentage formula. We can also see applications of percentage increase or percentage decrease in our daily life like increase in GDP or population increase or decrease and so on.