Question

A clock loses 12 minutes every 24 hours. It is set right at 7:25 p.m. on Monday. What will be the time when clock shows 1:45 p.m. the following day?

• A. 1:20:35 p.m
• B. 1:35:50 p.m.
• C. 1:25:35 p.m.
• D. None of these

Answer 1

The Correct Option is D

To solve the problem, we need to determine the actual time when the faulty clock shows 1:45 p.m. the following day. The clock loses 12 minutes every 24 hours. This means the faulty clock runs slower than the actual time.

Step 1: Determine the rate of time loss per hour

The clock loses 12 minutes in 24 hours. Therefore, the rate of time loss per hour is $\frac{12}{24}=0.5$ minutes per hour.

Step 2: Calculate the time elapsed on the clock

The time from 7:25 p.m. on Monday to 1:45 p.m. the following day is 18 hours and 20 minutes. This is calculated as:

• From 7:25 p.m. to 7:25 a.m. = 12 hours
• From 7:25 a.m. to 1:25 p.m. = 6 hours
• From 1:25 p.m. to 1:45 p.m. = 20 minutes

So, $12+6+(\backslash frac\{20\}\{60\})=18.3333$ hours.

Step 3: Calculate the actual time elapsed

Since the clock loses time, we need to calculate the actual time that would have elapsed. Using the rate of loss calculated in Step 1, for every hour, the clock shows 0.5 minutes less.

Actual time elapsed = clock time elapsed + loss = 18.3333 + (0.5 * 18.3333) / 60 = 18.3333 + 0.15 = 18.4833 hours.

Step 4: Calculate the actual clock time

Convert 18.4833 hours into hours and minutes:

• 18 hours remains as 18 hours.
• 0.4833 hours is converted to minutes: $0.4833\; *\; 60\; =\; 29$ minutes (approximately).

Therefore, 18 hours and 29 minutes have elapsed from 7:25 p.m. Monday.

The actual time is therefore:

7:25 p.m. + 18 hours = 1:25 p.m. on Tuesday + 29 minutes = 1:54 p.m. on Tuesday.

Conclusion

The correct actual time when the clock shows 1:45 p.m. is approximately 1:54 p.m., which is not among the given options. Therefore, the answer is "None of these".