Discussion
A clock is set right at 5 a.m. The clock looses 16 minutes in 24 hours. Then the true time when the clock indicates 10 p.m. on 4th day will be:
Answer: A
The true time will be 11 p.m.
From 5 a.m. on the first day to 10 p.m. on the fourth day, the clock shows 3 days and 17 hours, which is 89 hours. The clock loses 16 minutes a day, so it shows 1424 minutes for every 1440 true minutes.
\[ \begin{aligned} \text{true} &= 89 \times \frac{1440}{1424} \\ &= 89 \times \frac{90}{89} = 90\ \text{hours} \end{aligned} \]
90 true hours after 5 a.m. on day 1 is 11 p.m. on day 4, an hour later than the clock shows. A losing clock always shows less time than has passed, so the true time is later than 10 p.m., which rules out 8 p.m. and 9 p.m.; 12 p.m. overstates the loss.
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