Question

At what time between 5 and 6 are the hands of a clock coincident?

• A. 22 min 22 sec past 5
• B. 30 min past 5
• C. 22\(\frac{8}{11}\) min past 5
• D. 27\(\frac{3}{11}\) min past 5

Hint:

In clock problems, the relative speed of the hands helps in finding the time when the hands coincide or are opposite.

Answer 1

The Correct Option is D

Step 1: The minute hand moves 360° in 60 minutes, i.e., 6° per minute. The hour hand moves 360° in 12 hours, i.e., 0.5° per minute. Step 2: At 5 o'clock, the hour hand is at the 25th minute (5 × 5 = 25°). Step 3: For the hands to be coincident, the minute hand should cover a distance of \( 25° \) more than the hour hand. Step 4: The relative speed between the minute hand and hour hand is: \[ 6° - 0.5° = 5.5° \text{ per minute.} \] Step 5: The time taken by the minute hand to cover the 25° is: \[ \text{Time} = \frac{25}{5.5} = 27 \frac{3}{11} \text{ minutes.} \] Thus, the time when the hands coincide is 27\(\frac{3}{11}\) minutes past 5.