A clock, which gains uniformly, is 3 minutes slow at noon on Tuesday and is 5 minutes, 33 seconds fast at 3 pm on the following Tuesday. At what time was it showing the correct time?

Total time from Tuesday noon to next Tuesday 3 pm = 7 days + 3 hours = 171 hours. Total gain = 3 min + 5 min 33 sec = 8.55 minutes = 513 seconds. Gain per hour = 513 / 171 = 3 seconds/hour. To show correct time, it must gain 3 minutes (180 seconds). Time taken = 180 / 3 = 60 hours. 60 hours = 2 days and 12 hours. Tuesday noon + 2 days 12 hours = Friday 12 am.