Discussion

A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?

Answer: A

The clock gains, so it reaches 1 pm before the true time does.

From 8 am to 1 pm the next day is 29 hours on the clock. The clock's 24 h 10 min corresponds to 24 true hours:

\[ \text{true time} = 29 \times 60 \times \frac{1440}{1450} = 1740 \times \frac{144}{145} \]

\[ = 1728 \text{ minutes} = 28 \text{ h } 48 \text{ min} \]

\[ 8 \text{ a.m.} + 28 \text{ h } 48 \text{ min} = 12{:}48 \text{ p.m.} \]

So the true time is 48 minutes past 12.

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