Faulty Clocks

The questions framed on this topic will generally ask you to find:
- the time at which the inaccurate clock will show the correct time.
- the total time gained or lost in an inaccurate clock.
Definition
Faulty clock - A clock which gains or loses time.
If a clock indicates more than the actual time, then the clock is said to be fast or gaining time. E.g. if a clock indicates 10:15 when the correct time is 10, then it is 15 minutes too fast.
If a clock indicates less than the actual time, then the clock is said to be slow or losing time. E.g. if a clock indicates 09:45, when the correct time is 10, it is said to be 15 minutes too slow.
Coinciding time
Whenever a clock is too fast or too slow, then both the hands of the clock will not coincide at intervals of 66
If coinciding time > 65
And if coinciding time < 65
Q. How much time is gained/lost by a clock in 11 hours, if minute and hour hands of the clock overlap every 66 minutes?
(a) 6
(c) 5
Explanations :
Both hands of a clock overlap every 65
But the minute and hour hands of the clock in question overlap every 66 minutes.
Thus in 66 minutes, the time lost = 66 ๐๐๐ - 65
Then, time lost in 1 minute =
So, time lost in 60 minutes (i.e. in 1 hr) = 60 x
And time lost in 11 hours = 11 x
Answer: (b)