Faulty Clocks

clock

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 66 511 min

If coinciding time > 65511 then the clock is going slower than normal (i.e. clock is loosing time)

And if coinciding time < 65511 then the clock is going faster than normal (i.e. clock is gaining time).

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) 6 511 minutes (b) 5 511 minutes
(c) 5 911 minutes (d) 6 57 minutes

Explanations :

Explanation 1:

Both hands of a clock overlap every 65511 ๐‘š๐‘–๐‘› when the clock is working perfectly.
But the minute and hour hands of the clock in question overlap every 66 minutes.
Thus in 66 minutes, the time lost = 66 ๐‘š๐‘–๐‘› - 65511 ๐‘š๐‘–๐‘› = 611 minutes.

Then, time lost in 1 minute = 611 x 166 = 1121 minutes
So, time lost in 60 minutes (i.e. in 1 hr) = 60 x 1121 = 60121 minutes
And time lost in 11 hours = 11 x 1121 = 6011 min = 5511 minutes

Answer: (b)


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