Question

A clock is set right at 05:00 A.M. The clock loses 16 minutes in 24 hours. What will be the time when the clock indicates 10:00 P.M. on fourth day?

• A. 01:00 P.M.
• B. 02:00 P.M.
• C. 12:00 P.M.
• D. 11:00 P.M.

Hint:

For slow clock: Actual time = Clock time × (Actual rate / Clock rate) Always use proportional relation.

Answer 1

The Correct Option is D

Concept: A clock losing time means it runs slower than actual time. Given: \[ 24 \text{ hours} \to 16 \text{ minutes lost} \] So clock shows: \[ 24\text{ hr} - 16\text{ min} = 23\text{ hr }44\text{ min} \] Step 1: Convert into minutes.
Actual time in one day: \[ 24 \times 60 = 1440 \text{ minutes} \] Clock shows: \[ 1440-16=1424 \text{ minutes} \] Ratio: \[ \frac{\text{Clock time}}{\text{Actual time}}=\frac{1424}{1440} \]

Step 2: Find total shown time.
From 5 A.M. to fourth day 10 P.M.: First 4 days: \[ 4 \times 24 = 96 \text{ hours} \] From 5 A.M. to 10 P.M.: \[ 17 \text{ hours} \] Total: \[ 96-24+17=89 \text{ hours} \] Clock indication: \[ 89 \text{ hours} \]

Step 3: Find actual time.
Actual time: \[ 89 \times \frac{1440}{1424} \] \[ =90 \text{ hours approximately} \]

Step 4: Add to starting time.
Starting at: \[ 05:00 A.M. \] After 90 hours: \[ = 11:00 P.M. \]

Step 5: Final conclusion.
Hence, correct answer is: \[ \boxed{11:00 P.M.} \]