A clock is set right at 10 am. If the clock gains 8 minutes uniformly in 24 hours, then what time will it show at 7 pm on the same day?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7:03 pm
A clock that gains time uniformly runs fast at a steady rate, so the time it gains grows in proportion to the time that really passes. It was set right at 10 am, so at that moment it showed the correct time and had gained nothing.
It gains 8 minutes in 24 hours, so in 1 hour it gains \(\frac{8}{24}=\frac{1}{3}\) minute (20 seconds)
From 10 am to 7 pm, 9 hours really pass
In those 9 hours it gains \(9\times\frac{1}{3}=3\) minutes, so it is now 3 minutes ahead of the correct time
When the correct time is 7 pm, a clock 3 minutes ahead shows 7:03 pm