**Important formulae and tricks and shortcuts of Problems On Clocks ****.****:**

**Clocks Concepts :**

The dial of the clock is circular in shape and was divided into 60 equal minute spaces

60 minute spaces traces an angle of 3600. Therefore, 1minute space traverses an angle of 60

In 1 hour, Minute hand traverses 60 minute space or 3600 ,Hour hand traverses 5 minute space or 300

The hands of the clock are perpendicular in 15 minute spaces apart

The hands of the clock are in straight line and opposite to each other in 30 minute spaces apart.

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

The hands of the clock are perpendicular to each other for 22 times in 12 hours and for 44 times in a day.

The hands of the clock are opposite to each other for 11 times in 12 hours and 22 times in a day.

The hands of the clock coincides with each other for 11 times in 12 hours and 22 times per day

The hands of the clock are 44 times in a straight line per day

The minute hand gain 55 minutes over hour hand per hour.

Hence x minute space to be gained by minute hand over hour hand can be calculated as x.(60/55) or x.(12/11)

**Important Formula and Equations:**

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

Hour Hand and Minute Hand: A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called minute hand or long hand .

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

In every hour, both the hands coincide once.

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

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

When the hands are in opposite directions, they are 30 minute spaces apart.

Angle traced by hour hand in 12 hrs = 360°

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

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

**For solved problems on above formulas please visit below sections:**