Answer :
Final answer:
The clock will display 12 minutes and 5 seconds past 3 p.m. when the actual time is 3 p.m., as it gains 10/24 minutes per hour and has been running for a total of 29 hours.
Explanation:
The question involves calculating the time displayed by a faulty clock that gains time over a specific period. We're given that a clock is set correctly at 10 a.m. and it gains 10 minutes over the next 24 hours. The goal is to figure out what the clock will display when the actual time is 3 p.m. the following day.
First, we need to calculate how many hours have passed from 10 a.m. to 3 p.m. the next day:
From 10 a.m. to 10 a.m. the next day is 24 hours.
From 10 a.m. to 3 p.m. the next day is an additional 5 hours.
In total, 24 + 5 = 29 hours have passed.
The clock gains 10 minutes in 24 hours, which is the same as gaining 10/24 minutes per hour. To find out how much time the clock has gained over 29 hours, we multiply the hourly gain by the total number of hours passed:
(10/24) minutes/hour × 29 hours = (10 × 29) / 24 minutes = 290 / 24 minutes = 12.0833 minutes
12.0833 minutes can be converted into minutes and seconds as follows:
12 minutes and 0.0833 × 60 seconds = 12 minutes and 5 seconds.
Therefore, when the actual time is 3 p.m., the clock will display 12 minutes and 5 seconds past 3 p.m., which corresponds to answer option C.