Question

Tick the most appropriate answer.
A train departs from Delhi railway station at $21:50$ hours every day. The time shown in your analogue watch at the departure will be
(A) \[2:50{\text{ a}}{\text{.m}}{\text{.}}\]
(B) $9:50{\text{ p}}{\text{.m}}{\text{.}}$
(C) $9:50{\text{ a}}{\text{.m}}{\text{.}}$
(D) $11:50{\text{ p}}{\text{.m}}{\text{.}}$

Answer 1

Hint: The time given in the question is of twenty four hour format, while we have to answer it in the twelve hour format. For converting the twenty four hour format to the twelve hour format, we have to subtract $12:00$ hours from the given time.

Complete step-by-step solution:
We know that an analogue watch has twelve equal marks marked on the complete circumference of the watch, with equal distance between two consecutive marks. Each mark corresponds to an hour. Between two consecutive marks, there are five sub smaller marks each of which indicate a minute.
Now, there exist two systems for measuring the time. One is the twenty four hour format, and the other is the twelve hour format. In the twenty four hour format, we do not have to worry about the state of the day, whether morning, noon, evening or midnight. This is because for each of the twenty four hours of the day, we have a separate numbering. But in the twelve hour format, one time can correspond to two different states of the day. So we use the designation AM and PM next to the time. The time of $12:00$ hours is chosen as the bridging of the two states of the day, and is called the mid day. The time post this time uses the designation of PM. And the time before this time uses the designation of AM.
Now, for converting the twenty four hour format to the twelve hour format we have two cases. If in the twenty four hour format, the time is less than or equal to $12:00$ hours, then we keep it as it is after adding AM next to it. But if the time is greater than $12:00$ hours, then we subtract $12:00$ hours from the time and add the PM next to it.
The time of $21:50$ hours given in this question is clearly greater than $12:00$ hours. So it corresponds to the PM. And for its value, we subtract $12:00$ hours from the given time to get
 \[t = \left( {21 - 12} \right):50{\text{ p}}{\text{.m}}{\text{.}}\]
$ \Rightarrow t = 9:50{\text{ p}}{\text{.m}}{\text{.}}$
Thus, the time shown in the analogue watch is $9:50{\text{ p}}{\text{.m}}{\text{.}}$

Hence, the correct answer is option B.

Note: The twenty four hour format is used in the documentation of car to avoid any chance of ambiguity in the medical history of a patient. But the countries which are English speaking use the twelve hour format, and also the mixture of the two formats.