Question

What time is $ 7\dfrac{1}{2} $ hours before $ 2:12 $ am?

Answer 1

Hint: In order to know the time before the given time, we need to change the values in $ 24 $ -hour clock cycle, by adding $ 12:00 $ in the time given. Then simply subtracting the hour and minute value separately. If needed to take carry, we would take $ 1 $ hour as carry and add it to the minutes value.

Complete step-by-step answer:
We are given the time $ 2:12 $ am.
First converting $ 2:12 $ , into $ 24 $ -hour clock.
Since, the time is asked $ 7\dfrac{1}{2} $ hours before $ 2:12 $ am, that means the time for the present and the next day $ 2:12 $ am. For that first $ 24 $ hours is completed for the first day and another $ 2 $ hours $ 12 $ minutes is going on, of the second day, so we add $ 24:00 $ to $ 2:12 $ and we get: $ 2:12 + 24:00 = 26:12 $ in the $ 24 $ -hour clock.
As we know that $ 1 $ hours hour is equal to $ 60 $ minutes. So $ \dfrac{1}{2} $ hour $ = 30 $ hours.
From this we can write $ 7\dfrac{1}{2} $ hours as $ 7:30 $ hours.
We need to find $ 7\dfrac{1}{2} $ hours before $ 2:12 $ am, so subtracting $ 7\dfrac{1}{2} $ , i.e $ 7:30 $ from $ 2:12 $ i.e $ 26:12 $ .
Since, we can see that minute value of $ 26:12 $ is less than that of $ 7:30 $ , so we would be adding $ 1 $ hour that is equal to $ 60 $ minutes to $ 00:12 $ from $ 26:00 $ .
So, we get the value: $ 26 - 1:12 + 60 = 25:72 $ .
On subtracting $ 07:30 $ from $ 2:12 $ i.e $ 25:72 $ , we get:
 $ 25:72 - 07:30 = 25 - 07:72 - 30 = 18:42 $
That is $ 18 $ hours and $ 42 $ minutes.
Converting the time again to $ 12 $ -hour clock by subtracting $ 12:00 $ from $ 18:42 $ , we get:
 $ 18:42 - 12:00 = 18 - 12:42 - 00 = 6:42 $ pm
Therefore, $ 7\dfrac{1}{2} $ hours before $ 2:12 $ am is $ 6:42 $ pm.
So, the correct answer is “ $ 6:42 $ pm”.

Note:
I.It’s important to know the difference between $ 12 $ and $ 24 $ -hour clock and their conversion.
II.Do not add only $ 1 $ hour to the minute, always add $ 60 $ minutes which is equal to $ 1 $ hour.
III.Always Cross check the time once, whether it's am or pm.