# ch-18 : clocks :- Introduction & Formula

The dial of the clock is numbered from 1 to 12 in such a ray that each subsequent number is equidistant (5 minutes spaces apart) from the preceding number. It has two needles own as minute hand and hour Minute Hand and. The distance between two consecutive numbers is 5 minutes. It means that the circumference of the clock measures 60 minutes spaces. When hour hand travels 5 minutes spaces, the minute hand travels 60 minutes spaces. In this way, by traveling 60 minutes spaces, the minute hand gains 55 minutes on the hour hand

### Properties of Clock

1.In 60 minutes the minute hand gains 55 minutes on the hour hand.

2.A clock is said to be too fast when it shows time more than that of shown by a correct clock. Likewise, a clock is said to be too slow when it shows time less than that shown by a correct clock.

3. Both the hands of clock are at right angle (when the distance between two hands measures 90°) when they are 15 minutes spaces apart. This situation occurs twice in one hour.

4. Both the hands of a clock are opposite to each other when they are 30 minute spaces apart. This situation occurs once in a hour.

5. The hands of the clock are in the same straight line when they are coincident or opposite to each other.

**Ex. 1. At what time between 7 and 8 0′ clock will the hands of a clock be in the same straight line, but not together?**

(a) 5 minutes past 7 (b) 5(2/11)minutes past 7

(c) 5(3/11)minutes past 7 (d) 5(5/11) minutes past 7

Sol.

Fig. 18.1 shows the positions of hands of the clock at 7 and Fig. 18.2 shows the positions of hands of clock when both the hands are opposite in the straight line. From Fig. 18.1, it is clear that both the hands are 25 minutes apart and to be in the straight line both the hands have to be 30 minutes apart. Now as per properties of the clock, minute hand gains 55 minutes space in 60 minutes. Hence, it will gain 5 minutes space in ( (60/55)x 5) minutes 5(5/11) minutes Therefore, the hands are in the same straight line, but not together at 5(5/11)minutes past 7

**Ex. 2. At what time between 5.30 and 6 0′ clock will the hands of a clock be at right angle?**

(a) 43(3/11)minute past 5

(b) 43(7/11)minute past 5

(c) 40 minute past 5

(d) 45 minute past 5