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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 .

Odd Days: We are supposed to find the day of the week on a given date. For this, we use the concept of 'odd days'. In a given period, the number of days more than the complete weeks are called odd days . Leap Year: (i). Every year divisible by 4 is a leap year, if it is not a century. (ii). Every 4th century is a leap year and no other century is a leap year.

Ordinary Year: The year which is not a leap year is called an ordinary years . An ordinary year has 365 days.

Counting of Odd Days: 1 ordinary year = 365 days = (52 weeks + 1 day.) . 1 ordinary year has 1 odd day.

1 leap year = 366 days = (52 weeks + 2 days) 1 leap year has 2 odd days.

100 years = 76 ordinary years + 24 leap years

= (76 x 1 + 24 x 2) odd days = 124 odd days.

= (17 weeks + days) = 5 odd days.

Number of odd days in 100 years = 5

Number of odd days in 200 years = (5 x 2)= 3 odd days.

Number of odd days in 300 years = (5 x 3) = 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) = 0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.