# Clocks And Calendar Formulas

## Best Formulas for Clocks and Calendars

We will be discussing Clocks and Calendar Formulas to help student with variety of formulas that they can use to solve several type of Questions.

### Clocks

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

Hour hand and minute hand: The smaller hand of a clock is called the hour hand or shorthand and the larger hand ( instead of one ) is called minute hand or long hand.

### Calendar

• What is an ordinary year?
The year which is not a leap year is called
an ordinary year. An ordinary year has 365 days.
• What is Leap Year?
A leap year has 366 days.
• Every year divisible by 4 is a leap year, if it is not a century.
• Every 4th century is a leap year and no other century is a leap year.
• What is meant by 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.

## Clocks and Calendar Formulas: Clocks

### Important Observations and Formulas of Clock :

• A clock is a complete circle having 360 degrees. It is divided into 12 equal parts i.e. each part is $\frac{360}{12} = 30$
•  As the minute hand takes a complete round in one hour it covers 360 degrees in 60 min. Minute Hand covers $\frac{360}{60} = 6 \frac{degree}{ minute}$
• Also, as the hour hand covers just one part out of the given 12 parts in one hour, this implies Hour Hand covers 300 in 60 min. i.e. 1/2 degree per minute.
• Therefore, the relative speed of the minute hand is $6 – \frac{1}{2} = 5\frac{1}{2}degrees$
• Every hour, both the hands coincide once. In 12 hours, they will coincide 11 times. It happens due to only one such incident between 12 and 1’o clock.
• The hands are in the same straight line when they are coincident or opposite to each other.
• When the two hands are at a right angle, they are 15-minute spaces apart.
• In one hour, they will form two right angles and in 12 hours there are only 22 right angles. It happens due to right angles formed by the minute and hour hand at 3’o clock and 9’o clock.
• When the hands are in opposite directions, they are 30-minute spaces apart.
• If a clock indicates 9.15, when the correct time is 9, it is said to be 15 minutes too fast. On the other hand, if it indicates 8.45, when the correct time is 9, it is said to be 15 minutes too slow.
• If both the hour hand and minute hand move at their normal speeds, then both the hands meet after $65\frac{5}{11} minutes$.
• 22 times in a day, the hands of a clock will be in a straight line but opposite in direction.
• 44 times in a day, the hands of a clock will be straight.
• 44 times in a day, the hands of a clock are at right angles.
• 22 times in a day, the hands of a clock coincide.
• When the minute hand is behind the hour hand, the angle between two hands at M minutes past H ‘o clock will be                                                                                         $30(H- \frac{M}{5}) + \frac{M}{2}degree$
• When the minute hand is ahead the hour hand, the angle between two hands at M minutes past H ‘o clock will be                                                                                         $30(H-\frac{M}{5}) – \frac{M}{2}degree$

## Clocks and Calendar Formulas: Calendar

### Important Observations and Formulas for Calendars:

•  A leap year has 366 days
• Every year divisible by 4 is a leap year, if it is not a century.
• Every 4th century is a leap year and no other century is a leap year.
• Counting odd days
1 ordinary year ≡ 365 days ≡ (52 weeks + 1 day)
Hence number of odd days in 1 ordinary year= 1.
1 leap year = 366 days = (52 weeks + 2 days)
Hence number of odd days in 1 leap year= 2.
100 years = (76 ordinary years + 24 leap years)
= (76 x 1 + 24 x 2) odd days
= 124 odd days.
= (17 weeks + 5 days)
= 5 odd days.
Hence number of odd days in 100 years = 5.
Number of odd days in 200 years = (5 x 2) = 10 = 3 odd days