Question

Three 24-hour clocks show the time to be 12 noon. One of the clocks is always correct one loses a minute every 24 hours and one gains a minute every 24 hours. How many days will pass before all three clocks show the correct time again?

Answer 1

There is one clock that shows the right time so we do not have to worry about the one which is always correct.

Talking about the second clock that loses a minutes in every 24 hours (or in a day), so after 60 days (since it has lost 60 minutes because it is losing 1 minute everyday) it will show 11:00 a.m when it is exactly the noon.

So this way, in total it will take $60\times 24=1440$ days before it shows the correct noon.

Now, the third clock gains a minute every 24 hours (or in a day) , after 60 days (when it has gained 60 minutes or a complete hour) it will show 1:00 p.m when it is exactly the noon.

This way, it will take $60\times 24=1440$ days (since it has gained a minute everyday) when it shows the correct noon.

Therefore, it will take 1440 days before all the three clocks show the correct time again.