Question

A clock runs 6 minutes slow per day. By what percentage is it running slow?
a. 6
b. $\dfrac{1}{10}$
c. $\dfrac{12}{5}$
d. $\dfrac{5}{12}$
e. None of these

Answer 1

Hint: We will use the basic concept of clock, considering one complete day has 24 hours and that 1 hour equals to 60 minutes. We will calculate the percentage of time lost using the formula, $\text{Percentage of time lost=}\dfrac{\text{minutes lost}}{\text{total minutes in a day}}\text{ }\!\!\times\!\!\text{ 100}$

Complete step-by-step solution:
It is given in the question that a clock runs 6 minutes slow per day. And we have been asked to find by what percentage it is running slow.
We know that 1 complete day has 24 hours, also, we know that 1 hour is equal to 60 minutes. So, the total number of minutes in one complete day will be equal to the total number of hours in a day multiplied by 60 minutes. So, we get the total number of minutes in a day as follows,
$24\times 60=1440\text{ minutes}$
Now, we know that percentage of time lost can be calculated using the formula, $\text{Percentage of time lost=}\dfrac{\text{minutes lost}}{\text{total minutes in a day}}\text{ }\!\!\times\!\!\text{ 100}$
So, we have the minutes lost as 6 minutes and we know that the total minutes in a day is equal to 1440 minutes. So, we get,
\[\begin{align}
  & \text{Percentage of time lost=}\dfrac{6}{1440}\text{ }\!\!\times\!\!\text{ 100} \\
 & \text{=}\dfrac{600}{1440} \\
 & =\dfrac{5}{12} \\
\end{align}\]
Therefore, we get the percentage of the time lost is equal to \[\dfrac{5}{12}\].
Hence, option (d) is the correct answer.

Note: Most of the students usually make mistakes by not converting the hours into minutes and as a result, they write as $\dfrac{6}{24}\times 100$ and this is wrong. So, the students have to remember that while solving questions like this, always make sure that all the values are in the same unit. So, in this question, either one can convert minutes into hours or hours into minutes.