## Calendars

For solving questions on Calendars, read the following conventions:

- Ordinary year: An year in which the number of days is 365
- Leap year. A year in which the number of days is 366. As you know, it is February that has the one extra day.
- 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 in-day 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:

- 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.
- 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.

## Clocks

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:

- As you already know, the analog clock consists of two needles on its face. The face of an analog clock is also called dial.
- The shorter needle is the Hour hand and the longer one is the Minute hand.
- Both the minute hand and the hour hands will complete 3600 after one full rotation around the dial.
- The hour hand takes 12 hours to rotate once around the dial. The minute hand takes 60 minutes to rotate once around the dial.
- 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 3600. In 1 hour it rotates 300

**The Minute Hand: **In 60 minutes, the minute hand rotates 3600. In 1 minute it rotates 60

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 600. Again in the extra 20 minutes, it rotates by another 100. Therefore, the hour hand will have traversed 60 + 10 = 700 across the dial when the time is 2: 20 pm.

**Now, the Minute Hand**

In 1 minute it rotates 60, and in 20 minutes, 1200. Therefore, the angle between the minute hand and the hour hand when the time is 2:20 pm is 1200 – 700 = 500(clockwise direction).