General Aptitude: Clock & Calendars

Clock and Calendar

Clocks: Important formula and equations:

A clock has two hands, hour hand and minute hand – the hour hand is the smaller one and the minute hand is the larger one.
A clock is a complete circle having 3600. It is divided into twelve equal parts that are each part is 360° /12 = 30°
A minute hand takes one hour to complete around and it covers 3600 in 60 min. So, in 1min. it covers 360° /60 = 6° per min.
After every one hour, both hands coincide once. In 12 hours, both the hands coincide 11 times since between 1 1 and 1, they coincide only once i.e., at 12 o’clock.
When the two hands are at the right angle, they are 15mins spaces apart. The hands are in the same straight line when they are coincident or opposite to each other.
In 1 hour, they will form two right angles and in 12 hours they will form 22 right angles.
The angle formed by both the minute and hour hand at 3 o’clock and 9 o’clock.
When the hands are in opposite directions, they are 30 min spaces apart.
If a clock indicates 7.15, when the correct time is 7, it is said to be 15 mins too fast.
Also, if a clock indicates 6.45 when the correct time is 7, it is said to be 15 mins too slow. The minute hand gains 55 mins over hour hand per hour.
22 times in a day, the hands of a clock will be in a straight line but opposite in direction. 22 times in a day, the hands of a clock coincide.
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.

Some common type of questions asked in the exam,

To find the angle between the two hands (i.e., minute hand and hour hand) at a given time.
To find the time when the angle between the two hands is given.
Questions on losing or gaining the time.

Calendar: Important formula and equations:

As we know that a Calendar measures a day, a week, a month, and a year. In an ordinary year, there are 365 days. The year which is not a leap year is an ordinary year.

Leap year: a year which is divisible by 4, if it is not a century year.

Odd days: In a given period, the number of days more than the complete weeks.

Counting of odd days: In an ordinary year, there are 365 days, and in that there are (52 weeks + 1 day). This additional day is called an odd day.

So, in 1 Leap year, there are 366 days which means (52 weeks + 2 days) this shows that there are 2 odd days in 1 leap year.

In 100 years = 76 ordinary years (non- leap years) + 24 leap years

= 76 × 1 + 24 × 2 = 124 odd days.

Since 7 odd days make a week, so by dividing 124 by 7 we get the number of odd days in 100 years that will be 5 (which is the remainder).

Thus, calculating as above; the number of odd days in 200 years is 5 × 2 = 10 – 7 (1 week)

= 3 odd days.

The number of odd days in 300 years is 5 × 3 = 15 – 14 (2 weeks) = 1 odd day.
The number of odd days in 400 years is {5 × 4 + 1 (leap century) – 21} = 0 odd days.
Likewise, each one of 800 years, 1200 years, 1600 years, 2000 years, and so on has 0 odd days.

Given below is the table showing days of the week related to odd days.