Basic FormulasRule 1Rule 2 |

**Formula / Rule / Type basic-formulas :-**

**Introduction**

**hour spaces**. Each hour space is further divided into 5 parts, called

**minute spaces**. This way, the whole circumference is divided into 12 x 5 = 60 minute spaces.

The time taken by the hour hand (smaller hand) to
cover a distance of an hour space is equal to the time taken
by the minute hand (longer hand) to cover a distance of the
whole circumference. Thus, we may conclude that **in 60 minutes,
the minute hand gains 55 minutes on the hour hand**

**Note:**The above statement (given in bold) is very much useful in solving the problems in this chapter, so it should be remembered. The above statement wants to say that:

In an hour, the hour-hand moves a distance of 5 minute spaces whereas the minute-hand moves a distance of 60 minute spaces. Thus the minute-hand remains 60 - 5 = 55 minute spaces ahead of the hour-hand

**Some other facts:**

1. In every hour, both the hands coincide once.

2. When the two hands are at right angle, they are 15 minute spaces apart. This happens twice in every hour.

3. When the hands are in opposite directions, they are 30 minute spaces apart. This happens once in every hour.

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

5. The hour hand moves around the whole circumference of clock once in 12 hours. So the minute hand is twelve times faster than hour hand.

6. The clock is divided into 60 equal minute divisions.

7. 1 minute division = 360°/60° = 6° apart.

8. The clock has 12 hours numbered from 1 to 12 serially arranged.

9. Each hour number evenly and equally separated by five minute divisions (= 5 X 6°) = 30° apart.

10. In one minute, the minute hand moves one minute division or 6°.

11. In one minute, the hour hand moves 1/2°

12. In one minute the minute hand gains 5 1/2° more than hour hand.

13. When the hands are together, they are 0° apart.

Hence,

**Both hands** **Required Angle**

to be coincident 0°

to be at right angle 90°

to be in opposite direction 180°

to be in straight line 0° or 180°

**Too Fast And Too Slow:**

If a watch indicates 9.20, when the correct time is 9.10, it is said to be 10 minutes too fast. And i f it indicates 9.00, when the correct time is 9.10, it is said to be 10 minutes too slow.

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. 1. In 60 minutes, the minute hand gains 55 minutes on the hour hand. 2. In every hour, both the hands coincide once. 3. The hands are in the same straight line when they are coincident or opposite to each other. 4. When the two hands are at right angles, they are 15 minute spaces apart. 5. When the hands are in opposite directions, they are 30 minute spaces apart. 6. Angle traced by hour hand in 12 hrs = 360°. 7. Angle traced by mintite hand in 60 min. = 360°. Too Fast and Too Slow : If a watch or a clock indicates 8.15, when the correct time
is 8, it is said to be 15 minutes too fast.On the other hand, if it indica tes 7.45, when the correct time is 8, it is said to be 15 minutes too slow. |

Basic FormulasRule 1Rule 2 |