How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?
Answer & explanation
Answer: (a) 3 times
The hands coincide once every 12/11 hours, and in this window that happens at about 10:54:33, 12:00 and 1:05:27. There is no separate meeting in the 11 o’clock hour, because the meeting after 11 falls exactly at 12:00.
- The hands coincide every 12/11 hours = 65 5/11 minutes, counting from 12:00.
- Working back and forward from 12:00: 10:54 6/11, 12:00 and 1:05 5/11; the next one, 2:10 10/11, is after 2:00 p.m.
- So the hands coincide 3 times between 10:00 a.m. and 2:00 p.m.
- Check: the hands meet only 11 times in 12 hours, so one hour-slot (11 to 12) has no meeting of its own.
Remember · Hands coincide 11 times in 12 hours; the meetings of the 11 o’clock and 12 o’clock hours are the same one, at 12:00.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·