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 $\frac{5}{11}$ min

If coinciding time > 65$\frac{5}{11}$ then the clock is going slower than normal (i.e. clock is loosing time)

And if coinciding time < 65$\frac{5}{11}$ 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 $\frac{5}{11}$ minutes (b) 5 $\frac{5}{11}$ minutes
(c) 5 $\frac{9}{11}$ minutes (d) 6 $\frac{5}{7}$ minutes

Explanations :
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