At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other?
Answer & explanation
Answer: (d) Between 7:05 hours and 7:10 hours
At 7:00 the hour hand is 210° ahead of the minute hand, and the minute hand gains 5.5° every minute. The gap falls to 180° after 30 ÷ 5.5 = 5 5/11 minutes — just after 7:05.
- Angle between the hands = |30H − 5.5M| degrees (H = hour, M = minutes).
- At 7:00 the angle is 30 × 7 = 210°, and it shrinks by 5.5° each minute.
- 210 − 5.5M = 180 gives M = 30 ÷ 5.5 = 5 5/11 minutes.
- The hands are opposite at 7:05 5/11, i.e. between 7:05 and 7:10.
- Check: at 7:05 the angle is 210 − 27.5 = 182.5°, still above 180°.
Remember · Angle = |30H − 5.5M|; the minute hand gains 5.5° a minute on the hour hand.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·