A clock was set on Monday at 8.30 a.m. On Tuesday, the following day, the clock showed 8.45 p.m. when the correct time was 8.30 p.m. How many minutes was the clock gaining in every 24 hours?

It gained 15 minutes in 36 hours.

15/36 = x/24

36x = 360

x = 10 minutes

To find out how many minutes the clock was gaining in every 24 hours, we need to calculate the difference between the actual time and the time shown on the clock.

First, let's calculate the difference between 8.30 a.m. on Monday and 8.30 p.m. on Tuesday:
12 hours (from 8.30 a.m. to 8.30 p.m.) = 720 minutes.

However, the clock showed 8.45 p.m. instead of 8.30 p.m., which means it gained an extra 15 minutes.

So, in a span of 12 hours, the clock gained 15 minutes.

To find the gain per hour, we divide the gain per 12 hours by 12:
15 minutes / 12 hours = 1 minute and 15 seconds (approximately) per hour.

Finally, to find the gain per 24 hours, we double the gain per hour:
1 minute and 15 seconds x 2 = 2 minutes and 30 seconds (approximately) per 24 hours.

Therefore, the clock was gaining approximately 2 minutes and 30 seconds in every 24 hours.

To determine the number of minutes the clock is gaining in every 24 hours, we need to find the difference between the time on the clock and the correct time over the course of 24 hours.

In this scenario, the clock was set on Monday at 8.30 a.m., and the following day (Tuesday), it showed 8.45 p.m. instead of the correct time of 8.30 p.m.

First, we need to calculate the time between when the clock was set on Monday at 8.30 a.m. and when the clock showed an incorrect time on the following day (Tuesday) at 8.45 p.m.:

1. Calculate the time difference in hours: 8.45 p.m. - 8.30 a.m. = 12 hours + 8 hours + 0.45 hours = 20.45 hours.

Next, we calculate the time difference in minutes:

2. Convert the fractional part of the hours to minutes: 0.45 hours x 60 minutes/hour = 27 minutes.

3. Add the minutes to the whole hours: 20 hours + 27 minutes = 20 hours and 27 minutes.

So, the clock gained 20 hours and 27 minutes between Monday at 8.30 a.m. and Tuesday at 8.45 p.m.

Now, we compare this time gain to a 24-hour period:

4. Calculate the ratio by dividing the time gain by the actual 24-hour period: (20 hours + 27 minutes) / 24 hours = 0.85 hours.

5. Convert the fractional part of the ratio to minutes: 0.85 hours x 60 minutes/hour = 51 minutes.

Therefore, the clock gains 51 minutes every 24 hours.

Note: It's important to note that this is based on the assumption that the clock is consistently gaining time at the same rate over a 24-hour period. If this is a one-time discrepancy, it may not accurately reflect the clock's overall time gain.