Clock and Calendar
Clock
and calendar are the basic instruments that are being used to measure time in
different units.
Clock
A clock is a circular/square shaped instrument used to
view/measure time in hours, minutes and
seconds.
Measurement
of times is an important aspect of out daily life. It helps us to prepare
our schedule and work in an orderly
manner. There are, mainly, four
important parts of a clock – Dial, Hour hand, Minute hand and Second hand,
The
Dial
The
dial of a clock is circular one, whose circumference is divided into 12 parts
(12 equal big divisilons) labeled as 1, 2, 3, 4, ........ and 12. The space
between every pair of two numbers is divided in 5 equal small divisions.
Thus,
the dial is divided into 60 small divisions. The clock has two hands. one is
longer (minute hand) and another is shorter is shorter (hour hand).
Minute
hand
The longer hand of the clock is known as minute hand. The minute
hand moves from one small division to the next small division in 1 min.
The
minute hand goes once round the dial in
1 h. Thus, the minute hand covers 60 small division in 1 h.
|
Hour hand
The
shorter hand of the clock is known as
hour hand. The hour hand moves from one number to the next number in 1 h. The
hour hand takes 12 h to complete one
round. Also, it takes 2 full rounds of the clock an a day. Its movement
is also in a clockwise direction.
1
day = 24 h
Second
hand we may come across some clocks or watches which have three hands. The
third hand which is very thin and is called the second hand.
The
second's hand makes full round in 1 min and the time in which it moves between
two successive small divisions is called 1 sec.
60 s = 1 min
Use of AM and PM
When
both the hands of a clock are at 12. The time is 12 )' clock. It may be in noon
or at midnight. If it is in the noon, we
say that the time is 12 noon. If it is at midnight, we say that the time is 12 midnight.
A day begins at 12 midnight and ends
at 12 midnight on the next day. Time between 12 midnight and 12 noon is denoted by AM, where AM stands for Ante- Meridian.
Thus,
4 AM refers to 4 o'clock in the morning. Time between 12 noon and 12 midnight
is denoted by PM. where PM stands for post-Meridian. Thus, 4 PM refers to 4
o'clock in the evening.
Types of Clocks
We
generally use 12 h clocks. The face of
these clocks is marked with numbers from
1 to 12 and the hour hand of the clock
goes round the dial (face) twice a day
(in 24 h).
But
Raiways, lines tine tables, Air lines time tables, shipping lines, Defance
forces and Television networks, etc do not use 12 h clock time. Instead they use 24 h clock time.
Digital watches also show 24 h clock time. A 24 h clock dial may be visualised
as the one given below.
The
use of 24 h clock time is very useful.
time is expressed by four digits. The
first two digits on the left denote hours while the right two digits denote
minutes. The day stares at 12 midnight and is written as 00000h. Hance, the
time in this clock type of is expressed as 12 o'clock midnight is written as
2400 h or 0000 h.
3: 00 am is written as 0300 h.
11:00 am written as 1100h.
2 : 00
pm is written as 1400 h.
Fast and slow
If
a watch or a clock indicates 6 :15, when
the correct time is 6, it is said to be
15 min fast. On the other hand, if it indicates 5 :45, when the correct time is
6, it is said to be 15 min slow.
Important Points
Ü in 60 min,
the minute hand gains 55 min on the hour
hand
Ü In every
hour, both the hands coincide once.
Ü The hands
are in the same straight line when they are
coincident or opposite to each
other.
Ü When the
two hands are at right angles (90°) they are 15 min space apart.
Ü When the
hands are in opposite directions, they are 30 min space apart.
Ü Angle
traced by hour hand in 12 h = 360°
Ü Angle
traced by minute hand in 60 min = 360°
Ü Both hands
of a clock occurs at right angle twice in
one hour, 22 times in 12 h hand 44 times in 24 h.
Ü Both hands
of a clock occurs in a straight line or are opposite once in one hour, 11 times in 12 h hand 22 times in24
h,
E.g.
At what angle the hands of a clock
are inclined at 15 min past 5?
(a) 72 (b) 67 (c) 58 (d) 64°
Solution: (b) At 15 min past 5, the minute hand is at 3 and hour and slightly ahead of 5.
Now, angle
through which hour shifts in 15 min = = 7
\ Angle at 15 min past 5 = = 67
E.g.
A clock is set right at 8 am. The clock gain 10 min in
24 h. What will be the right time when the clock indicates 1 pm on the
following day?
(a) 11
: 40 Pm (b)12 : 48 pm (c) 12 pm (d) 10 pm
Solution: (b) time from 8 am of a particular day to 1 pm on the following day = 29 h.
Now the
clock 10 min in 24 h, it means that 24 h. 10 min of this clock is equal to this
clock equal to 24 h of the correct clock.
h of this
clock = 24 h of the correct clock.
29 h of this clock = × 6 × 29 = 28
h, 48 min of correct clock
29 h of
this clock = 28 h 48 min of the correct clock It means that the clock in
question is 12 min faster than the
correct clock. Therefore, when clock indicates 1 pm the correct time will be 48
min past 12.
Calendar
The
record of all the days of the year is given in the calendar. It shows the
months, weeks and days in the year.
Week
days There are seven days in a week. A week starts with Monday and ends at
Sunday. After which again comes Monday. The same cycle foes on and on.
Month
of the year We know that, there are 12 months in a year. The months of the year
with the number of days in that month
are given below
|
Name of the months |
Number of days |
Name of the months |
Number of days |
|
1. January |
31 |
7. July |
31 |
|
2. February |
28 or 29 |
8. August |
31 |
|
3. March |
31 |
9. September |
30 |
|
4. April |
30 |
10. October |
31 |
|
5. May |
31 |
11. November |
30 |
|
6. June |
30 |
12. December |
31 |
February
of an ordinary year has 28 days. There are 365 days in an ordinary year.
Thus,
1 ordinary year = 365 days = 52 weeks and 1 day. February of a leap year
has 29 days, so, there are 366 days in a
leap year. Thus 1 leap year = 366 days = 52 weeks and days. A leap year comes
after every 4 yr.
Century
A block of 100 yr is called a century. A century has, thus a total of 100 yr.
Thus each one of the years 1100, 1800, 2000, 2100 is a century.
Lap
year, The year other than a century divisible by 4 as well as by 400 is called
a leap year.
Thus,
each one of the years, 1600, 1996, 2000,
20004, 2008 is leap year and none of the
years 1867, 1993, 1997, 1999, 2001, 2003, 2007 is a leap year/
ordinary
year The year which is not a leap year is called an ordinary year. Thus, each one of the years 1781, 1891, 1995,
1999, 2013 is an ordinary year.
Important
Points
Ü A leap year
has 52 weeks and 2 days.
Ü An ordinary
year has 52 weeks and 1 day. A year has
52 full weeks.
Odd
Days In a given period, the number of days more than the complete weeks are
called odd
Ü days. Also
when total number of days divided by 7 remainder called odd days.
Ü 1 ordinary year = 365 days = (52 weeks + 1 day)
Ü 1 leap year
= 366 days = (52 weeks + 2 days) 100 yr
= 76 ordinary years + 24 leap years = )76 × 1 + 24 × 2) odd days = 124 Odd days = (17 weeks + 5 days)
= 5 odd days.
Ü Number of
odd days in 100 yr = Number of odd days in 200 yr = (5 × 2) = 10 = (7 + 3) = 3
odd days.
Ü The first
day of century cannot be Wednesday, Friday and Sunday
Ü The last
day of century cannot be Tuesday and Saturday.
1. What
will be the angle between hour hand and minute hand, if clock shows 8:30
pm?
(a) 90° (b) 75° (c) 50° (d) 85°
2. Reaching
the place of meeting on Tuesday 15 min before 8:30 h, Anuj found himself ha/f
an hour earlier than the man who was 40 min late. What was the scheduled time
of the meeting?
(a) 8:00 h (b) 8:05 (c) 8:8:15 h (d) 8:45h
3. A clock
buzzes 1 time at 1 O'clock, 2 times at 1 O'clock, 3 times at 3 O. clock
and so on. What will be the total number
of buzzes in a day?
(a) 150 (b) 156 (c) 100 (d) None of these
4. How many
times are the hands of a clock is at right angle in a day?
(a) 22 (b) 24 (c) 44 (d) 48
5. How many
times do the hands of a clock coincide in a day?
(a) 24 (b) 22 (c) 21 (d) 20
6. How many
times do the hands of a clock points towards each other in a day?
(a) 24 (b) 20 (c) 12 (d) 22
7. If today
is Thursday, what will be the day on 363 days?
(a) Sunday (b) Saturday (c) Thursday (d) None of these
8. Today is
Monday. After 61 days, it will be
(a) Wednesday (b) Saturday (c) Tuesday (d) Thursday
9. Which of
the following is not a leap year?
(a) 707 (b) 800 (c) 1200 (d) 2000
10. Today is
Wednesday, what will be the day after 84 days?
(a) Monday (b) Tuesday (c) Wednesday (d) Sunday
11. Today is
Thursday. The day after 59 days will be
(a) Sunday (b) Monday (c) Tuesday (d) Wednesday
12. The last day of a century cannot be either
I) Tuesday II) Thursday III. Saturday IV. Sunday
(a) I and II (b) I and Iv (c) I,II and III (d) I,III and IV
13. The day
before the day before yesterday is three days after Saturday. What day is it
today? (a) Tuesday (b) Wednesday (c) Thursday (d) Friday
14. If
January 1 is a Friday, what is the first day of the month of March in a leap
year?
(a) Tuesday (b) Wednesday (c) Thursday (d) Friday
15. In a
month of 31 days, third Thursday falls on 16th, what will be the
last day of the month?
(a) 5th Friday (b) 4th
Saturday (c) 5th Wednesday (d) 5th Thursday
(e) None of these
16. A bus for Delhi leaves every 30 mantes from a
bus stand. An enquiry clerk told a passenger that the bus had already left 10
min ago and next bus will leave at 9:35 am. At what time did the enquiry clerk
give this information to the passenger?
(a) 9:10 am (b) 8:55am (c) 9:08am (d) 9:15am
17. Mrs
Susheela celebrated her wedding anniversary on Tuesday, 30th
September 1997. When will she celebrate
her next wedding anniversary on the same day?
(a) 30th September,2003 (b) 30th September,2004
(c) 30th September,2002 (d) 30th October,
2003
18. If
Republic day was celebrated in 1996 on Friday on which day in 2000 Independence
was celebrated?
(a) Tuesday (b) Monday (c) Sunday (d) Saturday
19. If 18th
February, 1997 falls on Tuesday, then what will be the day on 18th
February, 1999?
(a) Monday
(b) Tuesday (c) Thursday (d) Friday
20. I was
born on August 11. Mohan is younger to me by days. This year's independence day
falls on Monday. The day on which Mohan's birthday will fall this year will be
(a) Monday (b) Tuesday (c) Sunday (d) Thursday
Answer
with Explanations
1. (b)
Angle
= = 75°
2. (b) Anuj reached the place of meeting at 8:15 h,
he reached 30 min earlier than the man who was
40 min late. i.e. he reached 10 min late. Hence the scheduled time of
the meeting was 8: 05 h.
3. (c) Number of buzzes in a day = × 2 = 156
4. (c) IN 12h, they are at right angles, 22 times.
So, in 24 h, they are at right angles, 44 times.
5. (b) From the properties of the clock, we know
hour but between 11 O'clock and 1 O'clock, they coincide only once. Therefore, the hands of a clock
coincide 11 times in every 12 h.
Hence
, they will coincide (11 × 2) = 22 times in 24 h.
89h.
of this clock = 90 h of the correct clock Therefore, it is clear that in 89 h
this clock loses 1h and hence, the correct time is 11:00pm when this clock
shows 10:00pm.
6. (d) The hands of a clock point towards each other
11 times in every 12 h (because between 5 and 7, they point towards each other
only once at 6 O'clock).
Therefore
in a day the hands points 22 times in all, towards each other.
7. (d) Here, = 51 weeks + 6
days
8. (b) Each day of the is reputed after 7 days. So, after 63 days,
it will be Monday After 61 days, it
will be Saturday.
9. (a) The centre divisible by 400 is a leap year.
The year 707 in not a leap year.
10. (c) Everyday of the weeks is
repeated after 7 days. Hence it will be Wednesday after 84 days.
11. (a) Everyday of the week is reputed after 7 days. Hence, after 56 days, it would be Thursday
again and after 59 day 's, it would be
Sunday.
12. (c) The last day to century
cannot be either Tuesday, Thursday or Saturday.
13. (d) Three days after Saturday
is Tuesday and Tuesday is a day before a day before yesterday So, yesterday is
Thursday.
Hence,
today is Friday.
14. (a) Total number of days from
January 1 to March 1
=
31 + 29 + 1
=
61 days
(February
in leap years = 29 days) = 61 ¸ 7
=
8 weeks and 5 odd days
So,
the fifth day from Friday = Tuesday
15. (a) Friday will fall on 3, 10,
17, 24, 31 So, it will be 5th Friday on 31st
16. (d) Next bus
will leave at 9:35am. So, enquiry clerk gave the information to the passenger
at = (9: 05 + 0 :10) = 9:15am
17. (a) Total number of odd days
30
September, 1997 – 98 = 1
30
September, 1998 – 99 = 1
30
September, 1999 – 2000 = 2
30
September, 2000 – 01 = 1
30
September, 2001 – 02 = 1
30
September, 2002 – 03 =
\ Tuesday + 7 = Tuesday
So,
The next Tuesday will come on the Mrs sunshield's wedding anniversary in 3oth
September, 2003
18. (a) 26 January, 1996 to 15
August, 2000 days were = 1663
1663
having odd day = 4
\ in the year 2000, Independence day
=
Friday + 4 = Tuesday
19. (c) 18th February,
1997 is Tuesday. So17th February 1998 will also be Tuesday. Again 16th
February, 1999 with also be Tuesday.
Hence,
18th February, 1999 will be Thursday.
20. (a) Mohan was born on 31st July. August 15 falls on Monday.