In this chapter we are going to discuss the following topics with examples.

1. Clocks – Basics
2. Types of problems
3. Formulas
4. Examples

### CLOCKS - BASICS

1. A clock has two hands, the smaller one is called the hour hand and the larger one is called minute hand.
2. Angle traced by minute hand in 1 hr = 360°.
3. Angle traced by hour hand in 1hr = 30°
4. Speed of minute hand = 6° per min
5. Speed of hour hand = (½)° per min
6. The hour hand and minute hand coincides 22 times in a day. (Refer below picture)
7. The hour hand and minute hand will be in straight line and opposite (180°) 22 times in a day.
8. The hour hand and minute hand will be in right angle (90°) 44 times in a day.
9. If a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast. Similarly, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow. ## Don't watch the clock. Do what it does. Keep going...

Sam Levenson

#### TYPES OF PROBLEMS

1. Calculating the angle between Hour Hand and Minute Hand
2. Calculating the exact time during Straight line, Coincide & Right angle
3. Problems on incorrect clocks

#### FORMULA

To calculate angle between hour hand and minute hand

Angle= 11M/2 – 30H ,where M is minute and H is hour.

To calculate time during coincide, straight line and right angle.

A) Straight line (Coincide)            :           (5H+0) 12/11 (or) 60H/11

B) Right angle                              :           (5H+15) 12/11 minutes past H

C) Straight line (Opposite)            :           a. (5H-30) 12/11 minutes past H, when H>6

b.(5H+30) 12/11 minutes past H, when H<6

#### EXAMPLES

1.What will be the angle between hour hand and minute hand at 7.50?

a) 45° b)56° c)65°  d)75°

Answer: c) 65°

Solution : (11*50/2)- (30*7)  = 275-210 =65

2. At what time between 7 and 8’o clock will the hands of a clock in the same straight line but, not together?

a) 5 min. past 7 b)5  2/11 min. past 7    c)5  3/11min. past 7     d)5   5/11min. past 7

Answer : d)5   5/11min. past 7

Solution: (5*7- 30) *(12/11) =60/11 =5  5/11

3.A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?

a) 10 : 20 : 20 PM b) 10 : 23 : 20 PM c) 10 : 20 : 23 PM        d) 11 : 30 PM

Answer: b) 10 : 23 : 20 PM

Solution:

The watch gains 5 seconds in 3 minutes So 100 seconds in 1 hour. From 8 AM to 10 PM on the same day, time passed is 14 hours. In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the incorrect watch would show 10 : 23 : 20 PM

Thus in this post we have learned about the concepts of clocks and tips to solve the problems with examples.

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