A clock is set right at 4 a.m. It loses 16 minutes in 24 hours. What will be the correct time when the clock shows 9 p.m. on the 4th day (the day it was set being the 1st day)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10:00 p.m.
A clock that loses 16 minutes in 24 hours shows only 23 hours 44 minutes for every 24 real hours. So the real time passed is the time shown multiplied by \(\displaystyle\frac{24\text{ h}}{23\text{ h }44\text{ min}}\).
23 hours 44 minutes \(\displaystyle =23\frac{44}{60}=\frac{356}{15}\) hours
Time shown from 4 a.m. on day 1 to 9 p.m. on day 4 \(=3\) days 17 hours \(=3\times24+17=89\) hours
Real time passed \(\displaystyle =89\times\frac{24}{356/15}=89\times\frac{360}{356}=90\) hours
90 hours \(=3\) days 18 hours, and 4 a.m. + 3 days 18 hours = 10 p.m. on day 4