Analog clock is gaining 3 minutes every hour, you set it at 6 pm on saturday, when will it show the correct time

This is tricky.  Fasten your seat belt.  It's going to be a boompy ride.

If it's a 12-hour clock (doesn't show AM or PM), then it has to gain
12 hours in order to appear correct again.

How many times must it gain 3 minutes in order to add up to 12 hours ?

(12 hours) x (60 minutes/hour) / (3 minutes) = 240 times

It has to gain 3 minutes 240 times, in order for the hands to be in the correct positions again. Each of those times takes 1 hour.  So the job will be complete in 240 hours  =  10 days .

Check:

In 10 days, there are 240 hours.
The clock gains 3 minutes every hour ==> 720 minutes in 240 hours.
In 720 minutes, there are  720/60 = 12 hours       yay !


If you are on a military base and your clocks have 24-hour faces,
then at the same rate of gaining, one of them would take 20 days
to appear to be correct again.


Note:
It doesn't have to be an analog clock.  Cheap digital clocks can
gain or lose time too (if they run on a battery and don't reference
their rate to the 60 Hz power that they're plugged into).