**IMPORTANT FACTS**

The Face or dial of a
watch is a circle whose circumference is divided into 60 equal parts, called
minute spaces.

A clock has two hands. The
smaller one is called the hour hand or short hand while the larger one is
called the minute hand or long hand.

i) In 60 minutes, the
minute hand gains 55 minutes on the hour hand.

ii) In every hour, both
the hands coincide once.

iii) The hands are in the
same straight line when they are coincident or opposite to each other.

iv) When the two hands are
at right angles, they are 15 minute spaces apart.

v)When the hand's are in
opposite directions, they are 30 minute spaces apart.

vi)Angle traced by hour
hand in 12 hrs = 360°.

vii)Angle traced by minute
hand in 60 min. = 360°.

**Too fast and too slow:**If a watch or a clock indicates 8.15, when the correct time, 8 is said to be 15 minutes too fast.

On the other hand, if it
indicates 7.45, when the correct time is 8, it is said to be 15 minutes too
slow.

**SOLVED EXAMPLES**

1.
Find the angle
between the hour hand and the minute hand of a clock when 3.25.(47 ½ )

2.
At what time
between 2 and 3 o'clock will the hands of a clock be together?(10 10/11 minutes
pas 2)

3.
At what time
between 4 and 5 o'clock will the hands of a clock be at right angle? (5 5/11
minutes past 4 or 38 2/11 minutes past
4)

4.
Find at what time
between 8 and 9 o'clock will the hands of a clock being the same straight line
but not together. (10 10/11 minutes past 8)

5.
At what time
between 5 and 6 o'clock are the hands of a clock 3 min apart? (24 minutes past
5 or 31 5/11 minutes past 5)

6.
The minute hand
of a clock overtakes the hour hand at intervals of 65 minutes of the correct
time. How much a day does the clock gain or lose? ( 10 10/43 minutes in 24
hours)

7.
A watch which
gains uniformly is 6 min. slow at 8 o'clock in the morning Sunday and it is 6
min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct? (20min
past 7pm on Wednesday)

8.
A clock is set
right at 6 a.m. The clock loses 16 minutes in 24 hours. What will be the true
time when the clock indicates 10 p.m. on 4th day? (11 pm)

9.
A clock is set
right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time
when the clock indicates 1 p.m. on the following day? (48 minutes past 12)

**EXERCISE**

1.
A clock is
started at noon. By 10 minutes past 5, the hour hand has turned through:(155)

2.
An accurate clock
shows 8 o'clock in the morning. Through how many degrees will the hour hand
rotate when the clock shows 2 o'clock in the afternoon? (180)

3.
At 3.40, the hour
hand and the minute hand of a clock form an angle of: (135)

4.
The angle between
the minute hand and the hour hand of a clock when the time is 4.20, is: (75)

5.
The angle between
the minute hand and the hour hand of a clock when the time is 8.30, is: (10)

6.
At what angle the
hands of a clock are inclined at 15 minutes past 5? (67 ½ )

7.
The reflex angle
between the hands of a clock at 10.25 is: (197 ½ )

8.
How many times do
the hands of a clock coincide in a day? (22)

9.
How many times in
a day, the hands of a clock are straight? (44)

10.
How many times
are the hands of a clock at right angle in a day? (44)

11.
How many times in
a day, are the hands of a clock in straight line but opposite in direction?
(22)

12.
How much does a
watch lose per day, if its hands coincide every 64 minutes? (32 8/11)

13.
At what time, in
minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each
other? (16 4/11)

14.
At what time
between 9 and 10 o'clock will the hands of a watch be together? (49 1/11
minutes past 9)

15.
At what time
between 7 and 8 o'clock will the hands of a clock be in the same straight line
but, not together? (5 5/11 minutes past 7)

16.
At what time
between 4 and 5 o'clock will the hands of a watch point in opposite directions?
(54 6/11 minutes past 4)

17.
At what time
between 5.30 and 6 will the hands of a clock be at right angles? (43 7/11
minutes past 5)

18.
A watch which
gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at
2 p.m. on the following Monday. When was it correct? (2 pm on Wednesday)

19.
A watch which
gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the
same day, when the watch indicated quarter past 4 o'clock, the true time is: (4
pm)