Question

A clock is set right at 8 am. The clock gains 8 minutes in a day. What will be the true time when the watch indicates 11 am the next day?

• A. 50 minutes past 10 am
• B. 49 minutes past 10 am
• C. 48 minutes past 11 am
• D. 51 minutes past 10 am

Hint:

A clock that gains 8 mins/day is gaining \( \frac{1}{3} \) minute per hour. Over 27 hours, it gains roughly 9 minutes. Subtract 9 minutes from 11:00 am to get 10:51 am.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a problem of a faulty clock. The clock moves faster than the actual time. We need to find the ratio of faulty time to true time.
Step 2: Key Formula or Approach:
Gain = 8 minutes in 24 hours.
Total time shown by faulty clock = 24 hours 8 minutes for every 24 hours of true time.
Step 3: Detailed Explanation: 1. Total duration on the faulty clock: From 8 am today to 11 am next day = 27 hours.
2. Ratio: 24 hours 8 minutes of faulty time = 24 hours of true time.
3. Convert to minutes: \( (24 \times 60) + 8 = 1448 \) minutes faulty = 1440 minutes true.
4. For 27 hours (1620 minutes) faulty time:
\[ \text{True Time} = 1620 \times \frac{1440}{1448} \approx 1611.05 \text{ minutes} \] 5. 1611 minutes is roughly 26 hours and 51 minutes.
6. Adding 26 hours and 51 minutes to 8 am:
8 am + 24 hours = 8 am (next day).
8 am + 2 hours 51 minutes = 10:51 am.
Step 4: Final Answer:
The true time is 10:51 am, which is 51 minutes past 10 am.