A faulty wall clock is known to gain 5 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 13th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 14th July of the same year? A. 12:45 PM B. 12:58 PM C. 1:00 PM D. 2:00 PM
GATE 2018 · General Aptitude · Clock Time · medium
Answer: The correct time when the faulty clock shows 2 PM on 14th July is approximately 12:58 PM. Answer: B. 12:58 PM
- Establish the clock rate ratio: The clock gains 5 minutes per 24 real hours. So in 1440 real minutes, the clock advances 1445 minutes. Equivalently, for each clock-minute, real time advanced = 1440/1445 minutes.
- Find elapsed clock time from start to the shown time: From 9 AM July 13 to 9 AM July 14 = 24 hours. From 9 AM to 2 PM = 5 more hours. Total = 29 hours = 1740 clock-minutes.
- Convert to real elapsed time: real minutes = 1740 * 1440/1445 = 2505600/1445 = 1734.02... minutes ≈ 1734 minutes (to nearest minute). 1734 minutes = 28 hours 54 minutes.
- Add real elapsed time to start time: 9 AM + 28 hours = 1 PM (next day, same as 9 AM + 28 h = 13:00 on 14th July). 1 PM - 0 h wait + 54 min... 9 AM + 28 h 54 min = 9 AM + 28 hours + 54 min = 1:00 PM - 6 min = 12:54 PM. More precisely: 9:00 AM + 28 h 54 min: 9 + 28 = 37 hours = 1 day 13 hours = 10 PM that day... Let me recompute. 9 AM on 13th + 28 h 54 min: 9 AM + 24 h = 9 AM on 14th; 9 AM + 4 h = 1 PM on 14th; 1 PM - 6 min = 12:54 PM on 14th. Closest option is B. 12:58 PM.