The correct answer is option (A):
4 p.m. on Thursday
Here's how we can solve this problem:
First, let's determine the total time elapsed between the two observations.
From 4 p.m. on Wednesday to 4 p.m. on Thursday is 24 hours.
From 4 p.m. on Thursday to 4 p.m. on Friday is another 24 hours.
From 4 p.m. on Friday to 4 p.m. on Saturday is another 24 hours.
So, the total time elapsed is 3 days or 72 hours.
Now, let's consider how much the watch's error changed during this period.
At 4 p.m. on Wednesday, the watch was slow by 5 minutes. This means its actual time was 5 minutes ahead of the watch's time.
At 4 p.m. on Saturday, the watch was fast by 10 minutes. This means its actual time was 10 minutes behind the watch's time.
The total change in the watch's error is the difference between being 5 minutes slow and 10 minutes fast. This is a total change of 5 minutes (to catch up to the correct time) + 10 minutes (to become fast) = 15 minutes.
So, in 72 hours, the watch's error changed by 15 minutes. We want to find out when the watch showed the *right* time. This is the point where the error was 0 minutes.
The watch started by being 5 minutes slow. To reach the correct time (0 minutes error), it needs to gain 5 minutes.
We know that the watch gains 15 minutes in 72 hours.
We can set up a proportion to find out how long it takes to gain 5 minutes:
(Time taken) / (Minutes gained) = (Total time elapsed) / (Total minutes gained)
Time taken / 5 minutes = 72 hours / 15 minutes
Now, let's solve for "Time taken":
Time taken = (5 minutes * 72 hours) / 15 minutes
Time taken = (5 * 72) / 15 hours
Time taken = 360 / 15 hours
Time taken = 24 hours
This means that it took 24 hours from the initial observation (4 p.m. on Wednesday) for the watch to gain the 5 minutes needed to show the correct time.
So, if the watch was slow by 5 minutes at 4 p.m. on Wednesday, it would show the correct time 24 hours later.
4 p.m. on Wednesday + 24 hours = 4 p.m. on Thursday.
Therefore, the watch showed the right time at 4 p.m. on Thursday.
Let's check this.
At 4 p.m. on Wednesday, the watch is 5 minutes slow.
After 24 hours, at 4 p.m. on Thursday, the watch has gained some amount of time.
The total gain is 15 minutes over 72 hours, which is a rate of 15/72 minutes per hour.
In 24 hours, the watch gains (15/72) * 24 = 15/3 = 5 minutes.
So, if it was 5 minutes slow at 4 p.m. on Wednesday, after gaining 5 minutes by 4 p.m. on Thursday, it would be showing the correct time.
The final answer is 4 p.m. on Thursday.