Question

A watch which gains uniformly is 2 minutes slow at 10:00 AM on Monday and is $2\frac 12$ minutes fast at 1:00 PM the following day. When did it show the correct time ?

• A. 10:30 PM Tuesday
• B. 10:30 PM Monday
• C. 10:45 PM Monday
• D. 10:00 PM Monday

Answer 1

The Correct Option is D

The watch gains uniformly, which means it gains the same amount of time every hour. We are told that:

• At 10:00 AM on Monday, the watch is 2 minutes slow.
• At 1:00 PM on Tuesday, the watch is 2.5 minutes fast.

The total time between 10:00 AM on Monday and 1:00 PM on Tuesday is 1 day and 3 hours, or 27 hours. During this time, the watch gains 4.5 minutes (from being 2 minutes slow to being 2.5 minutes fast).

To calculate the rate of gain, we divide the total time gained by the total time passed:

Rate of gain $= \frac{4.5 \text{ minutes}}{27 \text{ hours}} = \frac{1}{6} \text{ minutes per hour}.$

Now, to determine when the watch showed the correct time, we know that the watch was 2 minutes slow at 10:00 AM on Monday. We need to find when it gained those 2 minutes to reach the correct time. The time taken to gain 2 minutes is:

Time taken to gain 2 minutes $= \frac{2 \text{ minutes}}{\frac{1}{6} \text{ minutes per hour}} = 12 \text{ hours}.$

Starting from 10:00 AM on Monday, adding 12 hours brings us to 10:00 PM on Monday, which is when the watch shows the correct time.