When the hands coincide — Aptitude Question
When the hands coincide: How many times do the hands of a clock coincide in 24 hours? Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 90 seconds
Question
How many times do the hands of a clock coincide in 24 hours?
Options
- 20
- 22
- 24
- 44
Show the answer and the worked solution
Correct answer: B. 22
Worked solution
- In 12 hours the hands coincide 11 times — the expected 12 minus one, because there is no separate coincidence between 11 and 12.
- Over 24 hours that is 2 × 11 = 22.
Answer: 22.
The idea
The hands coincide 11 times in 12 hours and are opposite 11 times too. Both counts are one less than the naive answer for the same reason.
Shortcut. The minute hand laps the hour hand once every 12/11 hours (65 5/11 minutes), so 24 ÷ 12/11 = 22 meetings.
Common trap. "24" — assuming one meeting every hour; the meeting due between 11 and 1 happens only once, at 12, so each 12 hours loses one.