Chapter Notes: Clock and Calendar

Clocks

Look at the following clocks.

Here are some units for measuring time:

Telling the Time

To the Nearest 5 Minutes

• There are 60 marks on the clock face.
• Out of these marks, 12 are numbered.
• The numbers represent 5-minute intervals.
• When the minute hand points to 1, it means 5 minutes past the hour.
• When the minute hand points to 2, it means 10 minutes past the hour.
• This pattern continues around the clock, so each number increases the minutes by 5.

• There are subdivisions between the numbers on the clock dial.
• Each subdivision represents 1 minute.
• There are a total of 60 divisions on the dial, indicating 60 minutes.
• The minute hand makes one complete turn around the dial in 1 hour, which equals 60 minutes.

Now, read the following clocks:

To the Nearest Minute

Recall what we learned earlier by looking at these examples.

In Clock A, the minute hand has moved 23 divisions and the hour hand is between 10 and 11, so the time is 10:23 (twenty-three minutes past ten).

Similarly, times for Clock B and Clock C are read by counting minute divisions from 12 and noting the hour hand position.

Edurev Tips:

• When the minute hand is before 6, we read the time as "past" the hour.
• When the minute hand is after 6, we read the time as "to" the next hour.

Using A.M. and P.M. Time

The clock shows a time such as 8:25, but we cannot tell whether it is morning or evening from the clock alone.

• A day consists of 24 hours.
• In a 12-hour clock system, the hour hand makes two complete rotations in one day.
• The same clock time appears twice a day.
• To distinguish the two, we use a.m. and p.m.
• a.m. stands for ante meridiem and means the time from midnight until noon.
• p.m. stands for post meridiem and means the time from noon until midnight.
• For example, 8:25 in the morning is written as 8:25 a.m.
• The same clock time in the evening is written as 8:25 p.m.

Edurev Tips: A day begins at 12 midnight and ends at 12 midnight of the following day.

24-Hour Time Notation

• The 24-hour clock or 24-hour time system shows time from 12 midnight to 12 midnight the next day.
• Times are written as 0000 hours to 2400 hours (four-digit format where the first two digits are hours and the last two are minutes).
• Using 24-hour time avoids confusion between morning and evening times.

The table below shows 24-hour equivalents of 12-hour times:

• 8:35 a.m. = 0835 hours
• 3:15 p.m. = 1515 hours
• 11:40 a.m. = 1140 hours
• 11:50 p.m. = 2350 hours

Conversion of Time

Look at the clocks and tell what time they show.

Edurev Tips:

Converting from Hours to Minutes and Minutes to Hours

1. Hours to minutes:1 h = 60 min

   Examples:
   (a) 5 h = 5 × 60 min = 300 min
   (b) 2 h 45 min = 2 h + 45 min = 2 × 60 min + 45 min = 120 min + 45 min = 165 min

2. Minutes to hours:
   

   Examples:
   (a) 480 min = (480 ÷ 60) h = 8 h
   (b) 352 min = (352 ÷ 60) h = 5 h 52 min
   Or
   352 min = 300 min + 52 min = (300 ÷ 60) h + 52 min = 5 h + 52 min = 5 h 52 min

Operations on Measures of Time

1. Addition
Example 1: Add 6 hours 45 minutes and 11 hours 39 minutes.

Thus, 6 hours 45 minutes + 11 hours 39 minutes = 18 hours 24 minutes.
Think:
45 min + 39 min = 84 min
= 60 min + 24 min
= 1 h + 24 min

2. Subtraction
Example 2: Raju completes a painting in 6 hours 26 minutes and Rohit completes it in 4 hours 45 minutes. How much more time does Raju take to complete the painting?

You have to subtract 4 hours 45 minutes from 6 hours 26 minutes to find the required time.

Thus, Raju takes 1 hour 41 minutes more to complete the painting.
Think:
45 min cannot be subtracted from 26 min.
Borrow, 1 h = 60 min from 6 hours.
60 min + 26 min = 86 min
86 min - 45 min = 41 min
5 h - 4 h = 1 h

Elapsed Time

• Using 24-hour time notation makes it easier to calculate elapsed time.
• Elapsed time is the duration between two specific times.
• If you know the starting time and the duration, you can find the finishing time.
• If you know the finishing time and the duration, you can find the starting time.

Example 3: Mr Verma's office starts at 10 a.m. and closes at 6 p.m. How many hours does the office remain open?

Thus, Mr Verma's office remains open for 2 hours + 6 hours = 8 hours.

Example 4: A flight took off for Mumbai from New Delhi at 3:10 p.m. The plane landed in Mumbai at 4:55 p.m. What was the duration of the flight?

∴ Duration of the flight = 50 minutes + 55 minutes
                                    = 105 minutes = 60 minutes + 45 minutes
                                    = 1 hour + 45 minutes
∵ 1 hour = 60 min
Thus, the duration of the flight was 1 hour 45 minutes.

Example 5: How long is the time from
(a) 1542 hours to 2039 hours?
(b) 4:35 a.m. to 6:20 p.m.?

(a) The elapsed time is 2039 hours - 1542 hours.

Thus, the elapsed time is 4 hours 57 minutes.
(b) To find the elapsed time between 4:35 a.m and 6:20 p.m., first convert the time into 24-hour time.

Thus, the elapsed time is 13 hours 45 minutes.

Example 6: Find the time using a 24-hour clock.
(a) 4 hours 25 minutes after 2040 hours
(b) 8 hours 15 minutes before 2:35 p.m.

a) Add 4 hours 25 minutes to 2040 hours to find the required time.
20 h 40 min + 4 h 25 min
= 24 h 65 min = 24 h + 1 h + 5 min
= 1:05 a.m. (It becomes next day.) 1 h 5 min after 12:00 midnight.
(b) 2:35 p.m. = 1435 hours = 14 h 35 min
∴ Required time = 14 h 35 min - 8 h 15 min
                          = 6 h 20 min
= 0620 hours or 6:20 a.m.

Calendar

• A calendar is a way to keep track of the months, weeks and days in a year.
• The calendar for the year 2019 is shown below.

• A year consists of 12 months.
• One year has 365 days (in a common year).
• A year is made up of 52 weeks and 1 extra day in a common year.
• One day is the time the Earth takes for one full rotation on its axis.
• The standard unit of time for everyday use is one day.

Starting from the first day of the week, the names of the days are:

This cycle of days repeats again and again. The short forms are: Mon., Tues., Wed., Thurs., Fri., Sat., Sun.

If today is Monday, after 7 days it will again be Monday.

Months and Days

There are 12 months in a year: January, February, March, April, May, June, July, August, September, October, November and December.

The number of days in various months is as follows:

April, June, September and November have 30 days. The rest have 31 days, except February which has 28 days and 29 days in a leap year.

To find the number of days in a year:

(7 × 31) + (4 × 30) + (1 × 28) = total days in a common year.

• There are 365 days in a common year.
• Every four years, usually there is an additional day, and that year has 366 days; such a year is called a leap year.
• The extra day is added to February, making it 29 days in a leap year.
• Examples of leap years are 2004, 2008, 2012 and 2016.

What leap year comes next after 2016? You can find it by adding 4 to 2016 to get 2020.

1. A year is a leap year if it is divisible by 4.

2. If a year ends in 00, it is a leap year only if it is divisible by 400.

• The year 2000 is a leap year, but 1900 is not.
• To calculate the number of weeks in a year, divide 365 by 7.
• 365 ÷ 7 = 52 weeks and 1 extra day.

By studying the calendar, we learn:

The years from 1900 to 1999 form the twentieth century. The years from 2000 to 2099 form the twenty-first century.

Months and Years

• 12 months = 1 year.
• To convert 1 year 7 months into months: 1 year = 12 months; 12 + 7 = 19 months.
• To convert 20 months into years and months: 20 months = 12 months + 8 months = 1 year 8 months.

Solved Examples

Example 7: If 10 April 2018 was a Tuesday, what was the day on 30 April 2018?

The same day repeats after every 7 days. After 10 April the next Tuesdays are 17 April and 24 April.Therefore, 30 April 2018 was a Monday.

Example 8: Rahul is 4 years 8 months old. His sister Divya is 2 years 9 months elder to him. How old is she?

Divya's age = Rahul's age + 2 years 9 months
                    = 4 years 8 months + 2 years 9 months
                    = 6 years 17 months
                    = 6 years + 12 months + 5 months
                    = 6 years + 1 year + 5 months (12 months = 1 year)

 = 7 years 5 months.

Example 9: Piyush went to a project in London when he was 24 years and 5 months old. Now he is 33 years and 2 months old. How long has he been there?

Piyush stayed in London for: (33 years 2 months - 24 years 5 months)

Thus, Piyush stayed in London for 8 years 9 months.
5 months cannot be subtracted from 2 months. So, we borrow one year from 33 years. 1 year = 12 months; 12 + 2 = 14.
Subtract 5 months from 14 months and 24 years from remaining 32 years.

Number of Days Between Two Given Dates

To find the number of days between two dates, count the days remaining in the first month (excluding the start date if the question says "between"), then add full months in between, and finally add days in the last month (excluding the end date if required by the question).

For example, to findthe  number of days between 20 July 1947 and 2 October 1947:

Leave out 20 July. Count days from 21 July to 31 July = 11 days. Add full months August (31 days) and September (30 days). Leave out 2 October.

Note: Whether to count the first or the last day (or both) depends on the wording of the question.

Edurev Tips: If the question is "from 20 July to 2 Oct." (including start), then count days as 12 + 31 + 30 + 2 = 75 days.

Example 10: The football team reached England on 10 February 2017 and stayed for 45 days. Find the date on which the team returned?

Number of days the team stayed in England in February
= 19 days (10th February is also counted.)
(Count from 10 to 28: 11, 11, ..., 28)
Number of days the team stayed in England in March,
= 45 - 19 = 26 days
Thus, the team stayed till 26 March, 2017 and returned on 27 March 2017.

Example 11: Nishant started reading "Charlie and the Chocolate Factory" on 15 May. It took him 21 days to complete the book. On what day did he finish reading?

Number of days on which Nishant read the book in May = 31 - 14 = 17
(Here, 15 May is also counted.)
Number of days he read in June = 21 - 17 = 4.
Thus, Nishant finished reading the book on 4 June.