A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the dock shows the time 6:00 p.m. on Wednesday, what is the correct time?

The correct option is 5:36 p.m.

Let us analyze the problem step-by-step to understand why this option is correct.

Step 1: Understand the rate of the fast clock
The wall clock gains 10 minutes in every 24 hours.
This means that when 24 hours of correct (true) time have elapsed, the faulty clock will have moved ahead by 24 hours and 10 minutes.
Let us convert 24 hours and 10 minutes into hours:
24 hours + 10 minutes = 24 + 10/60 hours = 24 + 1/6 hours = 145/6 hours.
Therefore, 145/6 hours on the faulty clock is equivalent to 24 hours of correct time.

Step 2: Calculate the time elapsed on the faulty clock
The clock was set correct at 8:00 a.m. on Monday.
We need to find the correct time when the faulty clock shows 6:00 p.m. on Wednesday.
Let us compute the total duration shown on the faulty clock from 8:00 a.m. Monday to 6:00 p.m. Wednesday:
- From Monday 8:00 a.m. to Tuesday 8:00 a.m. = 24 hours
- From Tuesday 8:00 a.m. to Wednesday 8:00 a.m. = 24 hours
- From Wednesday 8:00 a.m. to Wednesday 6:00 p.m. = 10 hours
Total time elapsed on the faulty clock = 24 + 24 + 10 = 58 hours.

Step 3: Calculate the actual (correct) time elapsed
We can use a simple ratio to find the correct hours elapsed (let it be $x$):

$\frac{145}{6}\text{hours of faulty time}=24\text{hours of correct time}$

Therefore, 1 hour of faulty time is equivalent to:

$24\times \frac{6}{145}=\frac{144}{145}\text{hours of correct time}$

Now, for 58 hours of faulty time, the correct time elapsed is:

$x=58\times \frac{144}{145}\text{hours}$

We can simplify this by dividing 58 and 145 by their common factor, 29 (since 29 × 2 = 58 and 29 × 5 = 145):

$x=2\times \frac{144}{5}=\frac{288}{5}\text{hours}$

Converting this fraction into mixed numbers:

$\frac{288}{5}=57\frac{3}{5}\text{hours}$

This represents 57 hours and a fraction of an hour:
$\frac{3}{5}\times 60\text{minutes}=36\text{minutes}$.
So, the actual time elapsed is 57 hours and 36 minutes.

Step 4: Determine the correct time on Wednesday
We need to add 57 hours and 36 minutes to Monday 8:00 a.m.:
- Adding 48 hours (2 days) brings us to Wednesday 8:00 a.m.
- We have 9 hours and 36 minutes remaining to add (57 hours 36 minutes - 48 hours = 9 hours 36 minutes).
- Adding 9 hours to Wednesday 8:00 a.m. gives Wednesday 5:00 p.m.
- Adding the remaining 36 minutes gives 5:36 p.m. on Wednesday.

Thus, the correct time is 5:36 p.m.