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### Calendar and Clock

#### Calendar and Clock with Solution – For Interviews, Written, Competitive and Entrance Exams

We have discussed the clock and calendar sections in our previous articles. Now, let us check some calendar and clock test practice questions. Solving the calendar and clock test practice questions will understand the topic more and will help you solve the questions in the test itself. There are few sections given based on the types of questions asked.

### CLOCK

A clock has two hands: Hour hand and Minute hand. The minute hand (M.H.) is also called the long hand and the hour hand (H.H.) is also called the short hand.

The clock has 12 hours numbered from 1 to 12.

Also, the clock is divided into 60 equal minute divisions. Therefore, each hour number is separated by five minute divisions. Therefore,

#### Important Points-

• One minute division = = 6° apart, i.e. In one minute, the 60 minute hand moves 6°.
• One hour division = 6° × 5 = 30° apart, i.e. In one hour, the hour hand moves 30° apart.
•  Also, in one minute, the hour hand moves = apart.
• Since, in one minute, minute hand moves 6° and hour hand moves, therefore, in one minute, the minute hand gains 5more than hour hand.
• In one hour, the minute hand gains 5 × 60 = 330° over the hour hand. i.e. the minute hand gains 55 minutes divisions over the hour hand.

#### Relative position of the hands –

• The position of the M.H. relative to the H.H. is said to be the same, whenever the M.H. is separated from the H.H. by the same number of minute divisions and is on same side (clockwise or anticlockwise) of the H.H.
• Any relative position of the hands of a clock is repeated 11 times in every 12 hours.
• When both hands are 15 minute spaces apart, they are at right angle.
• When they are 30 minute spaces apart, they point in opposite directions.
• The hands are in the same straight line when they are coincident or opposite to each other.
• In every hour, both the hand coincide
• In a day, the hands are coinciding 22
• In every 12 hours, the hands of clock coincide 11 times
• In every 12 hours, the hands of clock are in opposite direction 11 times.
• In every 12 hours, the hands of clock are at right angles 22 times.
• In every hour, the two hands are at right angles 2 times.
• In every hour, the two hands are in opposite direction once.
• In a day, the two hands are at right angles 44 times.
• If both the hands coincide, then they will again coincide after 65 minutes e. in correct clock, both hand   coincide at an interval of 65 minutes.
• If the two hands coincide in time less than 65 minutes, then clock is too fast and if the two hands coincide in time more than 65 minutes, then   the clock is too slow.

#### NOTE:

ANOTHER SHORT-CUT FORMULA FOR CLOCKS

Where H = Hour, M = minute

### Calendar

Solar year consists of 365 days, 5 hrs 48 minutes, 48 seconds. In 47 BC, Julius Caesar arranged a calendar known as the Julian calendar in which a year was taken as 365  days and in order to get rid of the odd quarter of a day, an extra day was added once in every fourth year and this was called as leap year or Bissextile. Nowadays, the calendar, which is mostly used, is arranged by Pope Gregory XII and known as Gregorian calendar.

In India, number of calendars were being used till recently. In 1952, the Government adopted the National Calendar based on Saka era with Chaitra as its first month, in an ordinary year, Chaitra 1 falling on March 22 of Gregorian Calendar and in a leap year it falls on March 21.

#### REMEMBER

• In an ordinary year,

1 year = 365 days = 52 weeks + 1 day

• In a leap year

1 year = 366 days =52 weeks + 2 days

#### NOTE: First January I A.D was Monday. So we must count days from Sunday.

• 100 years or one century contains 76 ordinary years and 24 leap years.

⇒ [76 ×52 weeks+ 76 odd days]

+ [24×52 weeks+ 24 × 2 odd days]

= (76 + 24) × 52 weeks + (76 + 48) odd days

= 100 × 52 weeks + 124 odd days

= 100 × 52 weeks + (17 × 7 + 5) odd days

= (100 × 52 + 17) weeks+ 5 odd days

∴100 years contain 5 odd days.

Similarly, 200 years contain 3 odd days,

300 years contain 1 odd days,

400 years contain 0 odd days.

Year whose non-zero numbers are multiple of 4 contains no odd days; like 800, 1200, 1600 etc.

#### The number of odd days in months

The month with 31 days contains (4×7 + 3) i.e. 3 odd days and the month with 30 days contains (4×7+2) i.e. 2 odd days.

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