On a particular day, a library installed a new clock which gains time uniformly.
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On a particular day, a library installed a new clock which gains time uniformly. The librarian observes the clock on a Monday morning and notices that the clock is 10 minutes slow at 10:00 AM.
She then observes the clock again on the following Monday and notices that the clock is 10 minutes 50 seconds fast at 10:00 PM.
Analyse the given scenario and determine when this clock will show the correct time.
Show answer & explanation
The clock gains 1250 seconds over 180 hours. To show correct time, it must gain 600 seconds (10 minutes), requiring (600/1250)*180 = 86.4 hours after Monday 10:00 AM, which corresponds to Thursday at approximately 12:25 AM.
Step-by-step Derivation:
Step 1: Total elapsed time from Monday 10:00 AM to next Monday 10:00 PM is 7 days + 12 hours = 180 hours.
Step 2: Total time gained = 10 min + 10 min 50 sec = 1250 seconds.
Step 3: Required gain to correct time = 10 min = 600 seconds.
Step 4: Time elapsed = (600 / 1250) * 180 = 86.4 hours = 3 days, 14 hours, 24 minutes.
Step 5: Monday 10:00 AM + 86.4 hours lands on Thursday 12:24 AM (Option B).