Question

One watch is 1 minute slow at 1 pm on Tuesday and 2 minutes fast at 1 am on Friday. When did it show the correct time?
A. 5:00 am on Wednesday
B. 5:00 pm on Wednesday
C. 9:00 am on Wednesday
D. 9:00 pm on Wednesday

Answer 1

Hint: In the above problem, we are given a watch that is slow by a minute at 1 pm on Tuesday. The same watch becomes fast by two minutes at 1 am on Friday. Since the watch was 1 minute slow and now it is 2 minutes faster, that means the watch has gained 3 minutes in time from Tuesday to Friday. Thus, we have to find the time delay after which the watch gains 1 minute, so that it can show the correct time at that moment.

Complete step by step answer:
Given that, the watch is one minute slow at 1 pm on Tuesday. Then the watch becomes 2 minutes fast at 1 am on Friday. Hence, in between Tuesday and Friday, the watch has gained 3 minutes. So we have to find the time after which the watch gains 1 minute so that it shows the correct time. First we have to count the total number of minutes between 1 pm on Tuesday and 1 am on Friday. 1 am Tuesday to 1 am Thursday is two full days that is \[24 + 24 = 48\] hours. 1 am Thursday to 1 pm Friday is 12 hours. Therefore, there are \[48 + 12 = 60\] hours from 1 am Tuesday to 1 pm Friday.
Also \[60hrs = 60 \times 60\min = 3600\min \]
Hence, the watch gains 3 minutes per 3600 minutes.

Therefore, the watch will gain 1 minute after,
\[ \Rightarrow \dfrac{{3600}}{3} = 1200\min \]
Converting 1200 minutes into hours, we get
\[ \Rightarrow \dfrac{{1200}}{{60}} = 20\,hr\]
Hence the watch will show the correct time after 20 hours.
Adding 20 hours to the starting time 1 am Tuesday, we get
\[ \Rightarrow \] 1 am Tuesday + 20 hours = 1 pm Wednesday – 4 hours
Hence,
\[ \Rightarrow \] 9 am Wednesday
Therefore the watch will show the correct time at 9 am on Wednesday.

So, the correct option is C.

Note: The standard measuring unit or the S.I. unit of time is second. There are many other units which are also used commonly. They are second, minute and hour. There are 60 seconds in a minute and 60 minutes in an hour. To convert time duration from hours to minutes, we can multiply it by 60. Ex: a day is 24 hours. That means a day has \[24 \times 60 = 1440\] minutes.