Consider the following statements:
- 1.Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.
- 2.Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.
Which of the above statements is/are correct?
Answer & explanation
Answer: (c) Both 1 and 2
The hour and minute hands meet 16 4/11 minutes after 3 o’clock, i.e. between 3:16 and 3:17. The second hand catches the minute hand about 58.98 seconds after 4:58, i.e. before 4:59. Both statements are correct.
- At 3:00 the hour hand is 90° ahead of the minute hand. The minute hand moves 6° a minute and the hour hand 0.5°, so the minute hand gains 5.5° a minute.
- It catches up after 90 ÷ 5.5 = 180/11 = 16 4/11 minutes, about 3:16:22 — between 3:16 and 3:17. Statement 1 is correct.
- t seconds after 4:58, the minute hand is at the 58 + t/60 minute mark and the second hand at the t mark. They meet when t = 58 + t/60, i.e. t = 58 × 60/59 ≈ 58.98 s.
- That is before 4:59, so statement 2 is also correct.
- ✓ 1. The hands coincide at 3:16 4/11, inside the stated minute.
- ✓ 2. The second hand passes the minute hand about 58.98 seconds after 4:58, before 4:59.
Remember · Clock overlaps: gap ÷ relative speed. Minute hand gains 5.5° per minute on the hour hand.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·