Question

A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the correct approximate time when the clock indicates 10 p.m. on 4th day?

• A. 11 p.m
• B. 9 p.m
• C. 11 a.m
• D. 11.30 p.m

Hint:

A simple way to set up the ratio for faulty clocks: (Correct Time / Faulty Time) = (24 hours / (24 - time lost)). Then, Correct Time Elapsed = Faulty Time Elapsed \(\times\) (24 / (24 - loss)).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a problem about a faulty clock that loses time at a constant rate. We need to find the actual time elapsed when the faulty clock shows a certain amount of time has passed.
Step 2: Key Formula or Approach:
1. Calculate the total time elapsed on the faulty clock.
2. Find the relationship between the time measured by the faulty clock and the correct clock.
3. Calculate the actual time elapsed.
4. Determine the correct time.
Step 3: Detailed Explanation:
The clock is set at 5 a.m. on Day 1. We need the time when it shows 10 p.m. on Day 4.
Time elapsed on the faulty clock:
From Day 1, 5 a.m. to Day 4, 5 a.m. = 3 full days = \(3 \times 24 = 72\) hours.
From Day 4, 5 a.m. to Day 4, 10 p.m. = 17 hours.
Total time shown by the faulty clock = \(72 + 17 = 89\) hours.
Now, let's find the rate. The clock loses 16 minutes in 24 hours.
So, when 24 hours of correct time have passed, the faulty clock has only shown 23 hours and 44 minutes.
23 hours 44 minutes = \(23 \frac{44}{60}\) hours = \(23 \frac{11}{15}\) hours = \(\frac{356}{15}\) hours.
This means \(\frac{356}{15}\) hours on the faulty clock = 24 hours of correct time.
So, 1 hour on the faulty clock = \(24 \times \frac{15}{356}\) hours of correct time = \(\frac{90}{89}\) hours of correct time.
The faulty clock has shown 89 hours. Let's find the correct time elapsed:
Correct time = \(89 \times (\text{correct time per faulty hour})\)
Correct time = \(89 \times \frac{90}{89} = 90\) hours.
The actual time is 90 hours after the start time (Day 1, 5 a.m.).
90 hours = 3 days and 18 hours (\(90 = 3 \times 24 + 18\)).
Start time: Day 1, 5 a.m.
After 3 days, the time is Day 4, 5 a.m.
Now, add the remaining 18 hours to Day 4, 5 a.m.:
5 a.m. + 18 hours = 23:00, which is 11 p.m.
Step 4: Final Answer:
The correct time is 11 p.m. on the 4th day.