Question

A clock is set right at 5.00 am. This clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 pm on 4th day?

• A. 10.44 pm
• B. 11.00 pm
• C. 11.16 pm
• D. 11.30 pm

Hint:

For gain-loss clock problems, use the proportion: \[ \frac{\text{Clock Time}}{\text{True Time}} = \frac{\text{Clock Rate}}{\text{True Rate}} \] This method is faster and more accurate than calculating cumulative loss directly.

Answer 1

The Correct Option is B

Concept: A clock that loses time runs slower than a correct clock. In 24 hours of true time, the clock shows: \[ 24\text{ h} - 16\text{ min} = 23\text{ h }44\text{ min} = 1424\text{ min} \] Thus, \[ 1424 \text{ min (clock)} = 1440 \text{ min (true)} \]

Step 1: Find the time shown by the clock.
From 5:00 am to 10:00 pm on the 4th day: \[ 3 \text{ days} = 72 \text{ hours} \] and \[ 5\text{ am to }10\text{ pm}=17\text{ hours} \] Therefore, \[ 72+17=89\text{ hours} \] The clock has shown 89 hours.

Step 2: Convert clock time into true time.
\[ \text{True Time} = 89\times \frac{1440}{1424} = 90 \text{ hours} \] Thus the actual elapsed time is approximately 90 hours.

Step 3: Find the actual clock reading.
\[ 5:00\text{ am}+90\text{ hours} \] \[ =11:00\text{ pm} \] Using the exact ratio gives approximately \[ 11:00\text{ pm} \] \[ \boxed{11:00\text{ pm}} \]