Problems on Clocks Questions & Answers (Compiled from UPSC, SSC ,PSC ,IBPS previous question papers)

Angle traced by the hour hand in 6 hours=(360/12)×6

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.

5 min spaces are gained in  min  = min

so, Required time =  min  past 7

At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min

40 min. spaces are gained in 60/55×40 min = 43 7/11 min.

To be together between 9 and 10 o’clock, the minute hand has to gain 45 min.

spaces. 55 min. spaces gined in 60 min.

45 min. spaces are gained in [60 / 55 × 45] min. or 49 1/11 min.
 The hands are together at 49 1/11 min. past 9.

4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
 Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min

50 min. spaces are gained in  min. or 

 Required time =  min. past 4.

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

The minute hand of a clock overtakes the hour hand at intervals of M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.

Here M = 64. The clock gains or losses in a day by

=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)

=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.

In a 12 hour period, the minute hand makes 12 revolutions while the hour hand makes one. If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times. In a 24 hour day you get 2×22=44.

The hands of a clock coincide 11 times in every 12 hours 

(Since between 11 and 1, they coincide only once, 
i.e. at 12 o'clock). 
 The hands coincide 22 times in a day.