Three clocks were set to true time. First runs with the exact time. Second slows one minute/day. Third gains one minute/day. After how many days will they show true time again?

A. 360

B. 180

C. 720

D. 480

E. None of these

A faulty watch will show correct time when it is either 12 hrs ahead or 12 hrs behind. This is so because we are using a 12hr watch just to check the time and ignoring the am/pm aspect or date aspect.

C. 720

The second watch gains 1min in 1 day

It will gain 12hrs * 60 min = 720 min in 720 days

Similarly, the third watch will be 12hrs ahead in 720 days.

Thus in 720 days, all three watches will be showing the same time.