Question

There are two clocks on a wall, both set right at 10:00 a.m. One clock is losing 2 minute per hour and the other clock is gaining 3 minute per hour. If the clock which is losing 2 minutes per hour shows 3:00 p.m. the next day, what time does the clock gaining 3 minutes per hour show?
A) 5.30 p.m
B) 4.00 p.m
C) 4.15 p.m
D) 5.00 p.m

Answer 1

Hint: We know that one hour is equal to 60 minutes. One day is equal to 24 hours. One minute is equal to 60 seconds. Using these concepts we can solve the given problem. As the next day means we take 24 hours more and the given extra hours.

Complete step by step solution:
Now they have given that 2 clocks are set right at 10 a.m.
Since they are given the first clock they are losing 2 minutes per hour and showing the time 3:00 p.m. on the next day.
That is the difference in hour from 10 a.m and 3:00 p.m on the next day is given by \[(24 + 5)\] hours. That is 29 hours.
The difference in the hour is ‘x’.
\[
  60x - 2x = 29 \times 60 \\
  58x = 29 \times 60 \\
  x = \dfrac{{1740}}{{58}} \\
  x = 30 \;
\]
Thus the time of clock one is from 10 a.m more than 30 hours. That is 4 p.m.
Now the second clock is gaining 3 minute per hour. We have time in difference between two clock is 30 hour and it is gaining 3 minute per hour
\[3 \times 30 = 90\min \]. Extra time of the original time of the first clock.
\[90\min = 60\min + 30\min \]. That is 1hour 30 minute more than the original time of clock 1.
Hence the time in clock 2 is 5:30 p.m.
Hence the required option is A
So, the correct answer is “Option A ”.

Note: To solve this we need to know the time concept well and good. In the above we have explained every step. Since they have given that the two clocks are set at 10.am. We take this as a reference time to calculate the times of two clocks.