A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the correct approximate time when the clock indicates 10 p.m. on 4th day?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 11 p.m.
A clock that loses time runs slow at a steady rate, so the time it shows and the correct time always stay in the same ratio. In every 24 h of correct time, this clock shows only 24 h − 16 min = 23 h 44 min.
Ratio of time shown to correct time: 23 h 44 min : 24 h \(=1424:1440=89:90\)
Time the clock shows from 5 a.m. on day 1 to 10 p.m. on day 4: 3 full days (72 h) + 17 h \(=89\) h
For every 89 h the clock shows, 90 h have really passed, so the correct time passed is 90 h
90 h \(=3\) days 18 h, and 5 a.m. on day 1 + 3 days 18 h \(=\) 11 p.m. on day 4
Shortcut: The question asks for the approximate time, so the loss can be counted day by day.
From 5 a.m. on day 1 to 10 p.m. on day 4 is 3 days 17 h, about \(3\frac{3}{4}\) days
Loss \(\approx16\times3\frac{3}{4}=60\) min, that is, about 1 hour
The clock is about an hour behind, so when it shows 10 p.m. the correct time is 11 p.m.