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What percent of $15$ hours is $18$ seconds?
(A) $30\% $
(B) $\dfrac{1}{{30}}\% $
(C) $36\% $
(D) $\dfrac{1}{{36}}\% $

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Last updated date: 13th Jun 2024
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Answer
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Hint: Any percentage can only be found when the units are the same as both the values. So start with changing $15$ hours into seconds. One hour is equal to $3600$ seconds. Now divide the $18$ seconds by $\left( {15 \times 3600} \right)$ seconds. This will give the fraction and multiplying it by $100$ will give us the required percentage.

Complete step-by-step answer:
Here in this problem, we need to find what percentage of $15$ hours is $18$ seconds. And we need to find out which of the four given options is correct.
Before starting with the solution, we should understand the concept of percentage first. The word percentage comes from the word percent. If we split the word percent into its root words, we will see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred”. So, the percent is translated directly to “per hundred.”
In mathematics, a percentage is a number or ratio expressed as a fraction of $100$ . It is often denoted using the percent sign, $'\% '$ . A percentage is a dimensionless number (pure number); it has no unit of measurement.
So for example, if we want to find what percentage of $350$ is $50$ . We will first divide $50$ into $350$ parts and then the value of one part can be multiplied by $100$ to express it in form of a percentage.
$ \Rightarrow $ Percentage $ = \dfrac{{50}}{{350}} \times 100 = \dfrac{5}{{35}} = \dfrac{1}{7}\% $
But both the quantities should be in the same unit system to be compared and making fractions.
For changing $15$ hours into seconds, we should convert one hour into seconds and then multiply the factor.
$ \Rightarrow 15{\text{ hours}} = 15 \times 60{\text{ minutes}} = 15 \times 60 \times 60{\text{ seconds}}$
Percentage of $15$ hours is $18$ seconds $ = \dfrac{{18}}{{15 \times 60 \times 60}} \times 100$
Now this can be further simplified by dividing the numerator and denominator by $100$
$ \Rightarrow $ The required percentage of $15$ hours is $18$ seconds $ = \dfrac{{\dfrac{{18 \times 100}}{{100}}}}{{\dfrac{{15 \times 60 \times 60}}{{100}}}} = \dfrac{{18}}{{15 \times 6 \times 6}}$
This can be further simplified as:
$ \Rightarrow $ Percentage of $15$ hours is $18$ seconds $ = \dfrac{{18}}{{15 \times 36}} = \dfrac{1}{{15 \times 2}}$
Therefore, we get the required percentage $ = \dfrac{1}{{30}}\% $
Hence, the option (B) is the correct answer.

Note: In questions like this, utilizing the basic definition of percentage in solving the problem. We can also check the answer obtained by multiply this percentage by the whole, i.e. $\dfrac{{\dfrac{1}{{30}}}}{{100}} \times 15 \times 60 \times 60 = \dfrac{1}{{3000}} \times 15 \times 60 \times 60 = \dfrac{1}{5} \times 15 \times 6 = 18{\text{ seconds}}$ . So we can check our answer by again finding the percentage of the whole to find the part.