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Q68 (CISF/2025) Science & Technology › Basic Science (Physics, Chemistry, Biology)

In a clock, what is the time between 4:00:00 PM and 5:00:00 PM, when both the hour hand and the minute hand come together ?

Explanation

To determine the time when the hour and minute hands coincide between 4:00 PM and 5:00 PM, we calculate the time needed for the minute hand to close the initial angular gap.

  • At 4:00 PM, the minute hand is at 12 (0 minutes) and the hour hand is at 4 (20 minutes mark). The initial gap is 20 minutes spaces.
  • In 60 minutes, the minute hand gains 55 minutes spaces over the hour hand. Therefore, the relative gain is 55⁄60 or 11⁄12 minutes per minute.
  • The time required to close the 20-minute gap = 20 ÷ (11⁄12) = 20 × (12⁄11) = 240⁄11 minutes.
  • 240⁄11 minutes = 21 9⁄11 minutes.
  • Converting the fraction to seconds: (9⁄11) × 60 = 540⁄11 ≈ 49.09 seconds.

Thus, the hands come together at approximately 4:21:49 PM.

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