Question

At what time (to nearest second) immediately after 4 o'clock do the hands of a clock coincide?

• A. 04:20:00 o'clock
• B. 04:20:45 o'clock
• C. 04:21:49 o'clock
• D. 04:21:55 o'clock

Hint:

To calculate when the clock hands coincide, use the formula \( T = \frac{60 \times h}{11} \), where \( h \) is the hour.

Answer 1

The Correct Option is C

Step 1: Concept of Coincidence of Clock Hands.
The minute hand and hour hand of a clock coincide once every hour and 5 \(\frac{5}{11}\) minutes. Thus, the time interval between the coincident events after 4 o'clock is given by: \[ T = \frac{60 \times 4}{11} = 218 \, \text{minutes} \, 49.1 \, \text{seconds}. \] So, the time at which the hands will coincide after 4 o'clock is approximately \( 04:21:49 \) o'clock.

Final Answer: \[ \boxed{04:21:49 \, \text{o'clock}} \]