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 = ?

Answer: Option C

Time interval from 9 am on Monday to 8 : 30 pm on Wednesday.
$$\begin{array}{rl}& \text{ = }\left(24\times 2.5\right)-\text{0:30 hours }\\ & \text{ = 60}-\text{0}\text{:30 hours}\\ & \text{ = 59 hours 30 minutes}\\ & =59\frac{30}{60}\\ & =59\frac{1}{2}\\ & =\frac{119}{2}\text{ hours}\\ & \text{Also 24 hours}-\text{12 minutes}\\ & =\text{23 hours 48 minutes}\\ & =23+\frac{48}{60}\\ & =23\frac{4}{5}\\ & =\frac{119}{5}\text{ hours}\\ & \therefore \frac{119}{2}\text{ hours of this clock}\\ & =\frac{24\times 5}{119}\times \frac{119}{2}\\ & =60\text{ hours}\\ & \left(60-\frac{119}{2}\right)\text{ hours}\\ & \text{ = }\frac{120-119}{2}\text{ hours}\\ & \text{ = }\frac{1}{2}\text{ hours}\\ & =30\text{ minutes}\end{array}$$
Hence, the correct time is 30 minutes after 8:30 pm i.e., 9 pm