Shortcuts in Quantitative Aptitude for Competitive Exams – Clock and Calendar
- 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,
- One minute division apart,
ie. In one minute, the minute hand moves 6°.
- One hour division = 6° x 5 = 30° apart, ie. 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 more than hour hand.
- In one hour, the minute hand gains 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 once.
- In a day, the hands are coinciding 22 times.
- 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 minutes, i.e. in correct clock, both hand coincide at an interval of minutes.
- If the two hands coincide in time less than minutes, then clock is too fast and if the two hands coincides in time more than minutes, then the clock is too slow.
- Shortcut Approach for finding degrees minutes and hours is
Where, M = minutes and, H = Hours
- When value of θ becomes more than 360, subtract 360 from the value of θ and complete the calculation.
If a clock indicates 6 : 10, when the correct time is 6 : 00, it is said to be 10 minute too fast and if it indicates 5:50 when the correct time is 6:00, it is said to be 10 minute too slow.
- Also, if both hands coincide at an interval x minutes and , then total time gained
minutes and clock is said to be ‘fast’.
- If both hands coincide at an interval x minutes and , then total time lost
minutes and clock is said to be ‘slow’.
An ordinary year has 365 days. Every year which is divisible by 4, is a leap year and has 366 days, But century year has 365 days except for year divisible by 400 which has 366 days.
An ordinary year contains 365 days
[i.e., 52 weeks + 1 day i.e. 1 odd day]
A leap year contains 366 days
[i.e. 52 weeks + 2 days i.e. 2 odd days]
A century (100 years) contains
= 24 leap years + 76 ordinary years
= 24 x 2 + 76 = 124 odd days
= 17 weeks + 5 odd days
200 years contains 2 x 5 – 7 = 3 odd days
300 years contains 3 x 5 – 14=1 odd day
400 years contains 4 x 5+ 1- 21=0 odd days
First January, 1 A.D. was Monday.
A solar year contains 365 days 5 hours 48 minutes 48 seconds.
The first day of a century must either be Monday, Tuesday, Thursday or Saturday.
To find a particular day witihout given date and day
Following steps are taken into consideration to solve such questions
Step I Firstly, you have to find the number of odd upto the date for which the day is to be determined.
Step II Your required day will be according to the following conditions
- If the number of odd days = 0, then required day is Sunday.
- If the number of odd days = 1, then required day is Monday.
- If the number of odd days = 2, then required day is Tuesday.
- If the number of odd days = 3, then required day is Wednesday.
- If the number of odd days = 4, then required day is Thursday.
- If the number of odd days = 5, then required day is Friday.
- If the number of odd days = 6, then required day is Saturday.
February in an ordinary year gives no odd days, but in a leap year gives one odd day.