A clock is 2 minutes slow at 1:15 PM and 6 minutes fast at 7:15 PM. At what time (in PM) will it show the correct time?
Show answer & explanation
Correct answer: C
Explanation
Total Time Difference:
The clock went from being 2 minutes behind to 6 minutes ahead; this means it gained a total of 2 + 6 = 8 minutes.
Rate of Gain:
The clock gained 8 minutes over a period of 6 hours. Therefore, the time required to gain 1 minute is: 6 hours / 8 = 3/4 hours.
When will it show the correct time?
The clock will show the correct time once it has made up for its initial 2-minute delay.
Time required to gain 2 minutes = 2 × (3/4 hours) = 1.5 hours (i.e., 1 hour and 30 minutes).
Calculating the Exact Time:
Adding 1 hour and 30 minutes to the starting time (1:15 PM): 1:15 PM + 1:30 = 2:45 PM.
The clock will show the correct time at 2:45 PM.
The correct option is: C) 2:45