Question

Find the whole quantity if 70 % of it is 14 minutes.

Answer 1

Hint: Percentage is a fraction of 100. The formula to calculate the percentage of some number in another number is given by \[{\text{Percentage}} = \dfrac{{{\text{Required Value}}}}{{{\text{Total Value}}}} \times 100\% \]. Use this formula to find the whole quantity.

Complete step-by-step answer:
The percentage of a quantity means a fraction of the quantity expressed by taking a hundred as a whole. 100 % means the entire quantity or the whole. The word percent comes from the Latin word Per Cent where Cent means a hundred.
The percentage is just a convenient way to express a fraction with a hundred as a whole.
A percentage is a number expressed as a fraction of 100. It is calculated by multiplying the numeric of the ratio by 100.
When we need to find the percentage of a number in another number, we find the ratio of the required number to the number we consider as a whole and multiply it by 100.
Here, we are given the percentage and the required number, we need to find the number that is taken as the whole, which is 100%.
To find the whole value, we substitute the number and the percentage in the formula as follows:
\[{\text{Percentage}} = \dfrac{{{\text{Required Value}}}}{{{\text{Total Value}}}} \times 100\% \]
Hence, we have as follows:
\[{\text{70\% }} = \dfrac{{{\text{14}}}}{{{\text{Total Value}}}} \times 100\% \]
Solving for the total value, we have:
\[{\text{Total Value}} = \dfrac{{{\text{14}}}}{{70}} \times 100\]
Simplifying, we have:
\[{\text{Total Value}} = \dfrac{{\text{1}}}{5} \times 100\]
\[{\text{Total Value}} = 20\]
Hence, the whole value is 20.

Note: The most common mistake students do is to find 70 % of the number 14 but it is wrong. We need to find a number such that 70 % of that number is 14.