You have the misfortune to own an unreliable clock. This one loses exactly 24 minutes every hour. It is now showing 3:00am and you know that is was correct at midnight, when you set it.
The clock stopped 1 hour ago, what is the correct time now?
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June 8th, 2015 | Category: 
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5:12 AM
It is exactly 6 am.
It is 6am.
Saying “Loses 24 minutes”, is another way of saying “Moves 36 minutes every hour”. 36 is 60% of 60, so its moving at 60% speed. For the clock to progress 3 hours, 5 hours would need to have passed (3 is 60% of 5). So at 5am, the clock would have struck 3:00, and that was one hour ago so it is 6am now.
I agree with Taylor and Crabman has a good explanation of why that might be the case.
But also it could currently be 2 PM or 10 PM.
To get the current time as 10 PM, you would have set the clock to midnight almost two full days ago (46 hours ago). The clock would have run at 60% of its speed for 45 hours – which would have been 27 hours at 60% time. Then because it stopped an hour ago, it would now be 46 hours later or 10 PM.
If the clock thinks it has run for 48 + 3 hours since you set it at midnight, it would have run for 51 hours at 60% speed, or 85 hours of “real time” before stopping an hour ago, so then the current time would be 2:00 PM a little more than 3.5 days after setting the clock.
If the clock thinks it has run for 72 hours (or any other multiple of 3 full days including 0 days) before stopping to show 3AM 1 hour ago, the current time will be 6 AM.
Note the 10:00 PM and 2:00 PM situations would also re-occur depending how many full days the clock “thinks” it has run before stopping at 3:00 AM.
Changing your own time zone, going on, or off daylight savings time could all shift the answer to this riddle.
Taylor, you are today’s winner!
6:00am: since the clock is losing 24 minutes every hour, for every real hour that has passed, the clock will only show 36 minutes. Since the clock shows 3:00am, we know that 180 clock minutes have passed. This therefore equals 300 real minutes and hence 5 hours. The clock stopped 1 hour ago and the time must now be 6.00am.