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1. A clock is displaying correct time at 9 am on Monday. If the clock loses 12 minutes in 24 hours, then the actual time when the clock indicates 8 : 30 pm on Wednesday of the same week is = ?

A. 8 pm

B. 7 pm

C. 9 pm

D. 8 : 59 : 45 pm

Solution:

Time interval from 9 am on Monday to 8 : 30 pm on Wednesday.

\begin{aligned} = (24 \times 2.5) - 0:30 hours \\ = 60 - 0 :30 hours \\ =  59 hours 30 minutes \\ = 59 \frac{30}{60} \\ = 59 \frac{1}{2} \\ = \frac{119}{2} hours \\ Also 24 hours - 12 minutes \\ = 23 hours 48 minutes \\ = 23 + \frac{48}{60} \\ = 23 \frac{4}{5} \\ = \frac{119}{5} hours \\ ∴ \frac{119}{2} hours of this clock \\ = \frac{24 \times 5}{119} \times \frac{119}{2} \\ = 60 hours \\ (60 - \frac{119}{2}) hours \\ = \frac{120 - 119}{2} hours \\ = \frac{1}{2} hours \\ = 30 minutes \end{aligned}

Hence, the correct time is 30 minutes after 8:30 pm i.e., 9 pm

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