How many times do the hands of a clock coincide in a day?

Question

How many times do the hands of a clock coincide in a day?

1. A. 23
2. B. 12
3. C. 24
4. D. 22 (Correct answer)

Correct Answer

Option D — 22

Detailed Solution & Explanation

The correct answer is 22.

Key Points

• The hands of a clock coincide (overlap) 22 times in a full day (24 hours).
• In any 12-hour period the hands overlap only 11 times, not 12 — because between 11 o'clock and 1 o'clock the hands coincide just once, at exactly 12:00.
• Since a day has two such 12-hour cycles, the total is 11 × 2 = 22 times.

Additional Information

• in the same 24 hours, the hands are opposite (180° apart) 22 times and are at a right angle (90°) 44 times.
• Remembering that the overlap 'skips' once every 12 hours is the key to avoiding the common wrong answer of 24, so option (D) 22 is correct.