**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)