Reasoning :Clock and Calendar
Calendar: Import Points to remember
A calendar is a particular measure of time. The smallest unit of a calendar is a day which is the average time in which earth turns round once on its axis, The time in which earth travels round the sun is known as a solar year which consists of 365 days, 5 hours, 48 minutes and 47 ½ seconds or approximately 365.2422 days.
Generally we take the year consisting of365 days. The difference between a solar year and a common year is 0.2422 of a day. This difference is taken into .account every fourth year by adding a whole day. Thus every fourth year has a total of 366 days and this year. is called a leap year. This extra day is added to the month of February and as such in every leap year February has 29 days.
The number of days more than the complete number of weeks in a given period, are called odd days.
In an ordinary year (of 365 days) there are 52 weeks and one odd days. 2 In a leap year (of 366 days) there are 52 weeks and two odd days:Every year which is exactly divisible by 4 is called a leap year. e.g., 1988, 1996, 2004, etc.
Also every fourth century is a leap year. The other centuries, although divisible by 4 are not leap years. Thus for a century to be a leap year,it should be exactly divisible by 400.
e.g., 400, 800, 1600, etc.
To find the odd day divide the given number of days by 7; the remainder we get is taken as the odd days. for example, In 65 days, if we divide 65 by 7, we get 9 as quotient and 2 as remainder. ·Thus we say that 65 days, has 9 weeks and 2 odd days.
Clock: Import Points to remember
The clock is an instrument which indicates time at a moment. The face of a clock or watch is a circle which is divided in 60 equal parts called minute spaces. The clock has two hands, the smaller one is called hour hand as it denotes hours and the larger one is called minute hand as it indicates minutes. The hours are denoted from 1 to 12 and the minutes have marked from 1 to 60. In between every two successive hour marking, there are 5 minute marking.
It may be noted that:
1. In every hour, both the hands coincide once.
2 The hands are straight once and in this position the hands are 30 minutes space apart.
3. When the two hands are at right angle, they are 15 minute spaces apart. This happens twice in every hour.
4. The hands are in the same straight line when they are coincident or opposite to each other.
5.The hour hand moves around the whole circumference of clock once in 12 hours. So the minute
6.hand is twelve times faster than hour hand. In one minute, the minute hand moves one minute division or 6°.
7.In one minute, the hour hand moves ½°
8.In one minute the minute hand gains 5 ½° more than hour hand.
Clock and Calendar based questions :Solved Example
1.How many days were there in February in the year 1680.
(a) 28 days
(b) 29 days
(c) 30 days
(d) None of these
Ans. (b)
On dividing 1680 by 4, we get zero as the remainder.
Thus 1680 was a leap year. In a leap· year the month of February has 29 days.
2.Today is Friday. What will be. the day after 62 days?
(a)Friday
(b) Thursday
(c) Saturday.
(d) Monday
Ans. (b)
Each day of the week is repeated after 7 days.· Therefore after 63 days, it would by Friday. So
after 62 days, it would be Thursday.
3.How many years were there from 24th July 1972 to 5th October 1973 .
(a)1 (1/6 )
(b) 1 (1/5)
(c) 1 (1/4)
(d) 1 (1/3)
Ans. (b)
The total number of days from 24th July 19721 5th October 1973. ' = 438 days = 365 days.+ 73 days
= 1 year +(73/365) days= 1 year +(1/5)year
4.Find the total number of days of the month January,February and March of the year 1984
(a)45
(b)93
(c)92
(d)91
Ans. (d) 1984iscompletely divisible by 4. Thus 1984 was a leap year and February has 29 days. Total no. of days=31 +29+31 =91 days.
5.Find the angle between the hands of a clock when the time is 3 .25?
(a)47½°
(b)45°
(c)72½°
(d)75°
When the minute hand moves 60 minutes( or 1 hr), the hour hand turns, an angle of 30°.
Therefore angle turned by the hour hand in 25 minutes= (30/60)*25 = 12½°
Required angle = 60- 12½° =47½°.
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