Question

A clock is set right at 8 AM. This clock gains 10 minutes in 24 hours. What is the true time when the clock indicates 11 AM ?

• A. 11:01:58
• B. 10:45:15
• C. 10:59:15
• D. 10:58:45
• E. 10:58:15

Hint:

For fast/slow clock problems: True elapsed $= \frac{\text{correct rate}}{\text{clock rate}} \times$ indicated elapsed. A clock gaining $x$ min/day means every 1440 clock-min = $(1440 - x)$ true minutes.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The clock gains 10 minutes every 24 hours (1440 minutes). Use the relation: true time elapsed $= \frac{1440}{1450} \times$ indicated time elapsed.

Step 2: Detailed Explanation:
Clock shows 11 AM; set at 8 AM. Indicated elapsed = 3 hours = 180 minutes. Clock gains 10 min in 1440 min, so 1440 clock-minutes $=$ 1430 true minutes. True elapsed $= \frac{1430}{1440} \times 180 = \frac{1430 \times 180}{1440} = \frac{257400}{1440} = 178.75$ minutes $= 178$ min $45$ sec. True time $=$ 8:00 AM $+$ 178 min 45 sec $=$ 8:00 + 2h 58m 45s $=$ 10:58:45.

Step 3: Final Answer:
The true time is 10:58:45.