For solving questions on Calendars, read the following conventions:

1. Ordinary year:

An year in which the number of days is 365

2. Leap year.

An year in which the number of days is 366.

As you know, it is February that has the one extra day.

3. Odd day:

(The word odd day is a term coined for the purpose of solving questions in this topic, Calendars. Apart from this convention, I don’t think this word finds usage inday to day life)

Now, what is an Odd Day?

The one extra day left after a particular time period is divided into a certain number of weeks is termed an Odd day.

Example:

1. An ordinary year having 365 days can be divided into 52 weeks

(52×7 = 364) and 1 day. This 1 day is termed an “odd day”

An ordinary year is therefore said to have 1 odd day.

2. A leap year having 366 days can be divided into 52 weeks and 2 days. Therefore, a leap year is said to have 2 odd days.

The periphery of an Analog clock is marked with either Numbers from 1 to 12 or Roman Numerals.

Tests are fond of asking questions on Clocks.

So, let us equip ourself with the following few facts on this topic:

1. As you already know, the analog clock consists of two needles on its face. The face of an analog clock is also called dial.

2. The shorter needle is the Hour hand and the longer one is the Minute hand.

3. Both the minute hand and the hour hands will complete 360^{0} after one full rotation around the dial.

- 1. The hour hand takes 12 hours to rotate once around the dial
- 2. The minute hand takes 60 minutes to rotate once around the dial.

4. The angle of rotation formed by either the hour hand or the minute hand is measured clockwise between the position marked 12 (in a 12-hour analog clock) onthe dial and that at which the respective needle is located at the then time.

The Hour Hand:

In 12 hours, the hour hand rotates 360^{0}.

In 1 hour it rotates 300

The Minute Hand:

In 60 minutes, the minute hand rotates 360^{0}.

In 1 minute it rotates 6^{0}

Equipped with the above facts, let us solve a few simple questions on this topic:

1. What is the angle between the Hour hand and the Minute hand when the time is 2:20 pm on any day?

Solution:

**The Hour Hand**

In 2 hours, it rotates 60^{0}.

Again in the extra 20 minutes, it rotates by another 10^{0}

Therefore, the hour hand will have traversed

60 + 10 = 70^{0} across the dial when the time is 2: 20 pm.

**Now, the Minute Hand**

In 1 minute it rotates 60, and in 20 minutes, 120^{0}

Therefore, the angle between the minute hand and the hour hand when the time is 2:20 pm is 120^{0} – 70^{0} = 50^{0} (clockwise direction)

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