Between 7 and 8 o’clock, at what time will the hour and minute hands lie on the same straight line but point in opposite directions?

Between 7 and 8 o’clock, at what time will the hour and minute hands lie on the same straight line but point in opposite directions?

  1. ক) 7 hours 5 minutes 27 seconds
  2. খ) 7 hours 10 minutes 55 seconds
  3. গ) 7 hours 16 minutes 22 seconds
  4. ঘ) 7 hours 21 minutes 49 seconds

From the BPDB Assistant Engineer (CSE) October 2026 – Written (BUET) exam, question 18 of 30.

Comments (1)

Answer: ক. 7 hours 5 minutes 27 seconds

Minute hand: 6° per minute. Hour hand: 0.5° per minute, starting at 210° at 7:00. "Opposite" means 180° apart:

\((210 + 0.5m) - 6m = 180 \;\Rightarrow\; 5.5m = 30 \;\Rightarrow\; m = 5\tfrac{5}{11}\ \text{min}\)

5/11 of a minute ≈ 27.3 seconds, so about 7:05:27.

Shortcut: the hands are opposite 11 times in 12 hours; between h and h+1 o’clock, at (60/11)(h − 6) minutes past h for h ≥ 7 → (60/11)(1) = 5 5/11 minutes.

— rhs

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