Question:

The traffic lights at three different signal points change after every 45 seconds, 75 seconds, and 90 seconds respectively. If all change simultaneously at 7:20:15 hours, then they will change again simultaneously at

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For problems involving repeated events, find the LCM of the times involved to determine when they coincide again.
Updated On: Aug 18, 2025
  • 7:27:30 hours
  • 7:28:00 hours
  • 7:27:50 hours
  • 7:27:45 hours
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The Correct Option is C

Solution and Explanation

The least common multiple (LCM) of the three signal times 45, 75, and 90 seconds will give the time after which all lights change together again. First, factorize the times: \[ 45 = 3^2 \times 5, \quad 75 = 3 \times 5^2, \quad 90 = 2 \times 3^2 \times 5 \] The LCM is \( 2 \times 3^2 \times 5^2 = 450 \) seconds. Thus, after 450 seconds, or 7 minutes and 30 seconds, the lights will change again simultaneously. Adding 7 minutes and 30 seconds to 7:20:15 hours: \[ 7:20:15 + 7:30 = 7:27:45 \text{ hours} \] - Option (A) 7:27:30 hours: Incorrect. The time is a bit earlier than the correct value.
- Option (B) 7:28:00 hours: Incorrect. This is not the correct time.
- Option (D) 7:27:45 hours: This is the correct answer.
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