A watch, which gains 5 seconds every 3 minutes, is set right at 8 AM. In the…
2023
A watch, which gains 5 seconds every 3 minutes, is set right at 8 AM. In the afternoon the same day, when the faulty watch indicates 5:15, the actual time is
Answer: C. 5:00 PM — ConceptWhen a watch gains g seconds in every t seconds of real time, it records t + g seconds during t actual seconds. Therefore, indicated elapsed time…
- A.
6 PM
- B.
5:30 PM
- C.
5:00 PM
- D.
5:05 PM
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Show answer & explanation
Correct answer: C
Concept
When a watch gains g seconds in every t seconds of real time, it records t + g seconds during t actual seconds. Therefore, indicated elapsed time divided by actual elapsed time is (t + g)/t, so actual elapsed time equals indicated elapsed time multiplied by t/(t + g).
Application
The watch gains 5 seconds in 3 minutes = 180 seconds, so it records 185 seconds for every 180 actual seconds.
From 8:00 AM to the indicated 5:15 PM, the indicated elapsed time is 9 hours 15 minutes = 555 minutes.
Actual elapsed time = 555 × 180/185 = 555 × 36/37 = 540 minutes = 9 hours.
Hence, the actual time is 8:00 AM + 9 hours = 5:00 PM.
Cross-check
In 540 actual minutes, the gain is (540/3) × 5 seconds = 900 seconds = 15 minutes. Thus, after 9 actual hours the watch indicates 9 hours 15 minutes after 8:00 AM, which is 5:15 PM.
Result
The actual time is 5:00 PM.