Question

What percentage is $2$ minutes $24$ seconds an hour?

Answer 1

Hint: In the question, we will first convert the total time duration given to us in hours into seconds. We also convert the time duration whose percentage is to be found into seconds so that the method of finding the percentage becomes easy. Then, we calculate the percentage of the time duration using the formula $\frac{{Time\,Duration}}{{Total\,Time}} \times 100\% $ and substituting the known values into the formula.

Complete answer: Total time duration is $1$ hour.
So, we have to convert this time duration into seconds.
Number of minutes in one hour $ = 60\min $
Number of seconds in one minute $ = 60\sec $
So, number of seconds in one complete hour $ = $$60 \times 60\sec $
$ = 3600\sec $
Now, the time duration whose percentage is to be found is given to us as $2$ minutes $24$ seconds.
So, we know that one minute consists of sixty seconds.
Hence, the time duration in seconds $ = \left( {2 \times 60 + 24} \right)\sec $
Simplifying the calculations, we get,
$ = \left( {120 + 24} \right)\sec $
$ = 144\,\sec $
Now, Percentage can be found using the formula $\frac{{Time\,Duration}}{{Total\,Time}} \times 100\% $.
So, we get, $\frac{{144\sec }}{{3600\,\sec }} \times 100\% $
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow \frac{4}{{100\,}} \times 100\% $
Now, cancelling the $100$ in numerator and denominator, we get the percentage as,
$ \Rightarrow 4\% $
Hence, $2$ minutes $24$ seconds is $4\% $ of an hour.

Note:
There are various methods to find an answer to the given question, but the method described above is the simplest one. We can also consider solving the problem using the unitary method by taking the original time period as $100\% $ of itself and then computing the percentage of the time duration. One must know the basics of percentage and unit conversion to solve such problems. Work as many problems as possible to crack these types of problems in a limited time period.