Preperation of Time & Date



Question No 1

If a light flashes every 6 seconds, how many times will it flash in 3/4 of an hour?

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Solution!
3/4 of an hour = 3/4 * 60 * 60 = 2700! !Light will flash in 6 seconds = 2700/6 = 450 times.

Question No 2

What is the angle between the hands of a clock at 2:30?

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Solution!
Hour hand is nearly at 2!Minute hand is at 6! !Angle between 2 and 6 is 120 degree.! !Hour hand move 1/2 degree in one minute.! !In 30 Minutes hour hand will move 1/2 * 30 = 15 degree! !Hence, Angle between hands is 120 - 15 = 105 degree.

Question No 3

2012 January 1st is Sunday,then which day is the Indian Independence day of the same year.

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Solution!
30+ 29+ 31 + 30 + 31 + 30 + 31+15 = 227/7 = reminder = 3! !So, Independence day is Wednesday..

Question No 4

What will be the day of the week 15th August, 2010?

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Solution!
15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)! !Odd days in 1600 years = 0! !Odd days in 400 years = 0! !9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days = 4 odd days.! !From January to 15 August (31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days! !227 days = (32 weeks + 3 days) = 3 odd days.! !Total number of odd days = (0 + 0 + 4 + 3) = 7.! !Hence, Given day is Sunday..

Question No 5

An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

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Solution!
Angle traced by the hour hand in 6 hours = (360/12)*6 = 180 degree.

Question No 6

The angle between the minute hand and the hour hand of a clock when the time is 4:20, is ?

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Solution!
Angle traced by hour hand in 13/3 hrs = (360/12 * 13/3) = 130 degree! !Angle traced by minute hand in 20 min = (360/60 * 20) = 120 degree! !So, required angle = 130 - 120 = 10 degree.

Question No 7

Today is Monday.After 61 days, it will be ...

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Solution!
Each day of the week is repeated after 7 days.! !So, after 63 days, it will be Monday.! !Hence After 61 days, it will be Saturday..

Question No 8

What was the day of the week on 17th June, 1998?

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Solution!
17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)! !Odd days in 1600 years = 0! !Odd days in 300 years = (5 x 3) = 1! !97 years has 24 leap years + 73 ordinary years.! !Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.! !From January to 17 June (31 + 28 + 31 + 30 + 31 + 17) = 168 days! !168 days = 24 weeks = 0 odd day.! !Total number of odd days = (0 + 1 + 2 + 0) = 3.! !Hence Given day is Wednesday..

Question No 9

January 1, 2008 is Tuesday.What day of the week lies on Jan 1, 2009?

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Solution!
The year 2008 is a leap year. So, it has 2 odd days.! !1st day of the year 2008 is Tuesday (Given)! !So, 1st day of the year 2009 is 2 days beyond Tuesday.! !Hence, it will be Thursday..

Question No 10

If 7th of the month falls two days after Wednesday. What day of the week will precede the 18th of month?

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Solution!
On 7th the day is Friday. On 17 (day before 18) there will be Monday.

Question No 11

On 8th Feb, 2005 it was Tuesday.What was the day of the week on 8th Feb, 2004?

Select the correct answer


Solution!
The year 2004 is a leap year. It has 2 odd days.! !So, The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.! !Hence, this day is Sunday..

Question No 12

What is the angle between the hands of a clock at 3:35 pm?

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Solution!
At 3:35 hour hand is nearly at 3!Minute hand is at 7! !Angle between 3 and 7 is 120 degree.! !Hour hand move 1/2 degree in one minute.! !In 35 Minutes hour hand will move 1/2 * 35 = 17.5 degree! !Hence, Angle between hands is 120 - 17.5 = 102.5 degree.

Question No 13

11th of April falls on Tuesday, what day will the last day of the month April occurs.

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Solution!
Tuesday will be on 11, 18 and 25 then 30th April will be on Sunday..

Question No 14

On 8th Dec, 2007 Saturday falls.What day of the week was it on 8th Dec, 2006?

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Solution!
The year 2006 is an ordinary year. So, it has 1 odd day.! !So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.! !But, 8th Dec, 2007 is Saturday.! !Hence, 8th Dec, 2006 is Friday..

Question No 15

What is the angle between the hands of a clock at 8:50 am?

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Solution!
At 8:50 hour hand is nearly at 8!Minute hand is at 10! !Angle between 8 and 10 is 60 degree.! !Hour hand move 1/2 degree in one minute.! !In 50 Minutes hour hand will move 1/2 * 50 = 25 degree! !Hence, Angle between hands is 60 - 25 = 35 degree.

Question No 16

What is the angle between the hands of a clock at 4:20 pm?

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Solution!
At 4:20 hour hand is nearly at 4 but not perfectly at 4.!Minute hand is at 4! !If both hands are at 4 then angle is 0 degree.! !Hour hand move 1/2 degree in one minute.! !In 20 Minutes hour hand will move 1/2 * 20 = 10 degree! !Hence, Angle between hands is 0 + 10 = 10 degree.

Question No 17

What is the angle between the hands of a clock at 7 o'clock?

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Solution!
At 7 o'clock the minute hand points to 12 and hour hand points to 7.! !Angle between 7 and 12 is 150 degree..

Question No 18

It was Sunday on Jan 1, 2006.What was the day of the week Jan 1, 2010?

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Solution!
On 31st December, 2005 it was Saturday.!Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.! !So, On 31st December 2009, it was Thursday.! !Thus, on 1st Jan, 2010 it is Friday..

Question No 19

What is the angle between the hands of a clock at 9 o'clock?

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Solution!
At 9 o'clock the minute hand points to 12 and hour hand points to 9.! !Angle between 9 and 12 at the clock is 90 degree..

Question No 20

How many times in a day, are the hands of a clock in straight line but opposite in direction?

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Solution!
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).! !So, in a day, the hands point in the opposite directions 22 times..

Question No 21

The 15th of the month falls on the day preceding Sunday, on what day will the 6th of the month fall?

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Solution!
As on 15th of the month day is Saturday so on 8th the day will also Saturday. Hence on 6th of the month day will be Thursday(Two days before Saturday)..

Question No 22

March 1st is Wednesday. Which month of the same year starts with the same day?

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Solution!
March has 3 odd days!April has 2 odd days!May has 3 odd days!June has 2 odd days!July has 3 odd days!August has 3 odd days!September has 2 odd days!October has 3 odd days! !Total 21 odd days. 21/7 = 0. So November has start with the same day..

Question No 23

What was the day of the week on 28th May, 2006?

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Solution!
28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)! !Odd days in 1600 years = 0! !Odd days in 400 years = 0! !5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) = 6 odd days! !From January to 28 May (31 + 28 + 31 + 30 + 28 ) = 148 days! !So, 148 days = (21 weeks + 1 day) = 1 odd day.! !Total number of odd days = (0 + 0 + 6 + 1) = 7 = 0 odd day.! !Hence Given day is Sunday.

Question No 24

Given that on 27th February 2003 is Thursday.What was the day on 27th February 1603?

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Solution!
After every 400 years, the same day occurs.! !Thus, if 27th February 2003 is Thursday, before 400 years i.e., on 27th February 1603 has to be Thursday..

Question No 25

Our teacher has come out with another puzzle for her students. It is, "If three days ago was the day before Friday, What day will be after tomorrow?"

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Solution!
Three days ago was Thursday and today is Sunday, so the day after tomorrow will be Tuesday..

Question No 26

If 20th of February of a leap year falls on Thursday, what day of the week will be on 3rd of next March?

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Solution!
On 27th February there will be Thursday and by counting 4 days after it Monday falls on 3rd of March..

Question No 27

The last day of a century cannot be ...

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Solution!
100 years contain 5 odd days.! !So, last day of 1st century is Friday.! !200 years contain (5 x 2) = 3 odd days.! !So, Last day of 2nd century is Wednesday.! !300 years contain (5 x 3) = 15 = 1 odd day.! !So, Last day of 3rd century is Monday.! !400 years contain 0 odd day.! !So, Last day of 4th century is Sunday.! !This cycle is repeated.!Hence Last day of a century cannot be Tuesday or Thursday or Saturday..

Question No 28

If 14th August falls on Monday, then what will be the day on 14th September.

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Solution!
Monday will fall on 14, 21 and 28th August. By taking into account that August has 31 days 1st September will be fall on Friday. So, 7th and 14th September will be on Friday..

Question No 29

How many non-leap years are there from 1801 to 1900?

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Solution!
Leap year comes after 4 years!In one century there will be 24 leap years! !Hence, there will be 76 non leap years from 1801 to 1900..

Question No 30

Reaching a party day before yesterday, I found myself two days late. If day after tomorrow is Friday. On what day was the party scheduled to be held?

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Solution!
As day after tomorrow is Friday so tomorrow is Thursday, today is Wednesday, yesterday was Tuesday and day before yesterday was Monday. Today before the day before yesterday was Saturday. Hence party was scheduled on Saturday..

Question No 31

How many times are the hands of a clock at right angle in a day?

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Solution!
In 12 hours, they are at right angles 22 times! !So, In 24 hours, they are at right angles 44 times..

Question No 32

Which of the following is a leap year?

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Solution!
The century divisible by 400 is a leap year.! !So, The year 800 is a leap year..

Question No 33

How many times do the hands of a clock coincide in a day?

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Solution!
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).! !The hands overlap about every 65 minutes, not every 60 minutes. So, the hands coincide 22 times in a day..

Question No 34

What is the angle between the hands of a clock at 1 o'clock?

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Solution!
At 1 o'clock the minute hand points to the 12 and the hour hand points to the 1.! !So we need to find the angle between the 12 and the 1.! !There are 12 total numbers on the clock and total angle on complete turn of the clock is 360 degree, so each one must be 360/12 = 30 degree.! !So the angle between the hands of a clock at 1 o'clock is 30 degree..

Question No 35

How many degrees will the minute hand move, in the same time in which the second hand move 4800

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Solution!
Minute hand covers 480/60= 80.

Question No 36

At what angle the hands of a clock are inclined at 15 minutes past 5?

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Solution!
Angle traced by hour hand in 21/4 hrs = (360/12 * 21/4) = 157.5 degree! !Angle traced by minute hand in 15 min = (360/60 * 15) = 90 degree! !So, required angle = (157.5 - 90) = 67.5 degree.

Question No 37

What is the angle between the hands of a clock at 7:05 am?

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Solution!
At 7:05 hour hand is nearly at 7!Minute hand is at 1! !Angle between 7 and 1 is 180 degree.! !Hour hand move 1/2 degree in one minute.! !In 5 Minutes hour hand will move 1/2 * 5 = 2.5 degree! !Hence, Angle between hands is 180 - 2.5 = 177.5 degree.

Question No 38

How many years have 29 days in February from 2001 to 2100.

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Solution!
100th year is not a leap year.!So 24 February's has 29 days..

Question No 39

A clock is started at noon.By 10 minutes past 5, the hour hand has turned through ...

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Solution!
Angle traced by hour hand in 12 hrs = 360 degree! !Angle traced by hour hand in 5 hrs 10 min. i.e.,! 31/6 hrs = (360/12 * 31/6) = 155 degree.

Question No 40

Which of the following is not a leap year?

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Solution!
The century divisible by 400 is a leap year.! !So, The year 700 is not a leap year..

Question No 41

Which year has the same calendar as 1700 ?

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Solution!
Year 1700 has 1 odd day!1701 has 1 odd day!1702 has 1 odd day!1703 has 1 odd day!1704 has 2 odd day!1705 has 1 odd day! !Hence, 1706 will has same calender..

Question No 42

March 1st is Wednesday. Which month of the same year has the same calendar?

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Solution!
Odd days from March to October! !3 + 2 +3 +2 +3 +3 +2 +3 = 21/7 = 0.! !If odd day is 0 then next month has the same calendar.! !Hence, November will have same calender as March..

Question No 43

In the time in which the second hand covers 3960 degrees, how many degrees does the hour hand move?

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Solution!
3960/(360*2) = 5.5 degree! ! .

Question No 44

Seen through a mirror, the arms of a clock show 9:30 what is the actual time?

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Solution!
No answer description available for this question..

Question No 45

Which of the following is not a leap year?

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Solution!
The century divisible by 400 is a leap year.! !So, The year 600 is not a leap year..

Question No 46

What is the angle between the two hands of a clock when the time shown by the clock is 5:30 p.m. ?

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Solution!
q = 11/2 m ? 30h = 11/2 *30 - 30 *5 = 165-150 = 15 degree! ! .

Question No 47

The calendar for the year 2007 will be the same for the year ...

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Solution!
Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.! !Year 2007 has 1 odd day!2008 has 2 odd day!2009 has 1 odd day!2010 has 1 odd day!2011 has 1 odd day!2012 has 2 odd day!2013 has 1 odd day!2014 has 1 odd day!2015 has 1 odd day!2016 has 2 odd day!2017 has 1 odd day! !Sum = 14 odd days = 0 odd days.! !Hence, Calendar for the year 2018 will be the same as for the year 2007..

Question No 48

The day that will come two days after tomorrow will be Thursday. What was the day that Dawned two days before yesterday.

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Solution!
As the day, two days after tomorrow is Thursday so tomorrow is Tuesday and today is Monday and yesterday was Sunday. Hence the day two days before yesterday was Friday..

Question No 49

How many times in a day, the hands of a clock are straight?

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Solution!
In 12 hours, the hands coincide or are in opposite direction 22 times.! !So, In 24 hours, the hands coincide or are in opposite direction 44 times a day..

Question No 50

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through

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Solution!
Angle traced by hour hand in 12 hrs = 360 degree! !Angle traced by hour hand in 5 hrs 10 min. i.e., 31/6 hrs = (360/12 * 31/6) = 155 degree.

Question No 51

It would be Tuesday two days after tomorrow. What was two days before yesterday?

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Solution!
As the day, two days after tomorrow is Tuesday so tomorrow is Sunday and today is Saturday and yesterday was Friday. Hence the day two days before yesterday was Wednesday..

Question No 52

The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.

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Solution!
Time is 2.20.!Hour hand at 2 (nearly) and minute hand at 4.! !Angle between 2 and 4 is 60 degrees [(360/12) * (4-2)]! !Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through 1/2 degrees in a minute.! !Therefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees.

Question No 53

By how many degrees does the minute hand move in the same time, in which the hour hand move by 280?

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Solution!
28 * 2 * 6 = 336 degree.

Question No 54

If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?

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Solution!
The year 2004 is a leap year. So, it has 2 odd days.! !But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.! !So, the day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.! !Given that, 6th March, 2005 is Monday.! !Hence 6th March, 2004 is Sunday..

Question No 55

At 3:40, the hour hand and the minute hand of a clock form an angle of ...

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Solution!
Angle traced by hour hand in 12 hrs = 360 degree! !Angle traced by it in 11/3 hrs = (360/12 * 11/3) = 110 degree! !Angle traced by minute hand in 60 min. = 360 degree! !Angle traced by it in 40 min = (360/60 * 40) = 240 degree! ! So, Required angle (240 - 110) = 130 degree.

Question No 56

What is the angle between the minute hand and the hour hand when the time is 1540 hours?

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Solution!
Hour hand is nearly at 3!Minute hand is at 8! !Angle between 3 and 8 is 150 degree.! !In 40 Minutes hour hand will move 1/2 * 40 = 20 degree! !Hence, Angle between hands is 150 - 20 = 130 degree.

Question No 57

The angle between the minute hand and the hour hand of a clock when the time is 8:30, is ?

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Solution!
Angle traced by hour hand in 17/2 hrs = (360/12 * 17/2) = 255 degree! !Angle traced by minute hand in 30 min = (360/60 * 30) = 180 degree! !So, Required angle = (255 - 180) = 75 degree.

Question No 58

The reflex angle between the hands of a clock at 10:25 is

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Solution!
Angle traced by hour hand in 125/12 hrs = (360/12 * 125/12) = 625/2 degree! !Angle traced by minute hand in 25 min = (360/60 * 25) = 150 degree! !So, Reflex angle = 360 - (625/2 - 150) = 197.5 degree.

Question No 59

By how many degrees does the minute hand move in the same time, in which the hour hand move by 18 degree?

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Solution!
18*2 *6 = 216 degree! ! .

Question No 60

January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?

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Solution!
The year 2007 is an ordinary year. So, it has 1 odd day.! !1st day of the year 2007 was Monday.! !1st day of the year 2008 will be 1 day beyond Monday.! !Hence, it will be Tuesday..
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