Let us revise
 Time is a period which is measured in minutes, days, years, etc.
60 seconds= 1 minute
60 minutes= 1 hour
24 hours= 1 day
365 days= 1 year  Time can also be defined as a function that takes in three numbers, a day (1 to 31), a month (1 to 12), and a year (say 2004) and gives back an integer.
For example,
Consider 23/01/2018, this function has 3 numbers, a day (23), a month (01), and a year (2018). When time is defined in this way, it is also called a date.  When we convert higher units of time to its lower units, we multiply. When we convert lower units of time to higher units, we divide.
EXAMPLE 1: Write 4 hours 5 minutes 60 seconds in terms of seconds.
SOLUTION:
Converting hours & minutes into seconds we get:
4 hours= 4X60 minutes= 4X60X60 seconds= 14400 seconds
5 minutes= 5X60 seconds= 300 seconds
Adding all the units in seconds term we get:
= (14400+300+60) seconds
=14760 seconds
Hence, 4 hours 5minutes 60 seconds in terms of second is 14760 seconds.
EXAMPLE 2: Neha’s date of birth is the thirtieth day of the eighth month of the year nineteen ninetysix. Write it in date format.
SOLUTION:
The day is 30^{th} day
Month= 8th
Year= 1996
Therefore, Date of Birth= 30/8/1996 [Ans]
Finding number of days
 We know that a year has 365 days. But, some years have 366 days. Those years are called leap years. The extra day occurs in the month of February. Leap years occur at an interval of 4 years.
How do you know if a year is leap year? If a particular year can be divided by 4 leaving zero remainder, then the year is a leap year. For example, 1996÷4=499
with remainder 0. Hence, 1996 is a leap year.  There are total 12 months. They are, January(1), February(2), March(3), April(4), May(5), June(6), July(7), August(8), September(9), October(10), November(11), December(12).
 January, March, May, July, August, October, and December have 31 days. April, June, September, and November have 30 days. February has 28 days but during a leap year it has 29 days.
For example,
In the year 1996,
February has 29 days
because 1996 is a leap year.
Trivia: Easy way to remember which months have 31 days & which have 30 days
Consider the knuckles of your hand
EXAMPLE 1: How many days are there from September 23 to October 10.
SOLUTION: 1 23 30days
September has 30 days.
Number of days left to complete September= (3023) days= 7 days
We are considering the first 10 days of October.
Hence, total number of days between September 23 and October 10= (7+10) days
= 17 days [ANS]
EXAMPLE 2: Add 4 years 5months add 7 years 8 months.
Subtract 4 years 5 months from 7 years 2 months
SOLUTION: Addition:
 Add the digits in the months position.
 Here, 8+5= 13 months.
 But, there are 12 months in total.
 So, we will consider 13months= (12 months + 1 months) = ( 1 year + 1 month)
 Write 1 month in months position and add the remaining 1 year to the (7+4) years in the years position.

4 years 
5 months 

7 years 
8 months 
+ 
=11 years 
13 months(invalid) 

+1 year( extra 12 months from months position) 
12 months(carried to years position) 

12 years 
1 month 
Answer: 12 years 1 month
Subtraction:
 Subtract the digit in the months position
 Here, 25=3. But, 3 months makes no sense
 So, we will take 12 months (1 year) borrow from years position.
 Now, 3+12(borrowed months) = 9 months.
 In the years position, 74=3 years. But we took 1 year (12 months) borrow from years position. So, we have to subtract 1 year from years position. Thus, 31= 2 years

7 years 
2 months 

4 years 
5 months 
 
=3 years 
3 months (invalid) 

1 year(compensation for the borrowed 12 months) 
+12 months(borrowed) 

2 years 
9 months 
Answer: 2 years 9 months
Note: In addition of dates, 12months generates a carry of 1 year which is added in
years position. In subtraction, 1 year borrow from years position is added as 12 months in months position
Time Intervals
 Time can be represented in two formats: 24hour format and 12hour format.
24hour format: 00 hour, 01 hour, 02 hour, 03 hour, 04 hour, 05 hour, 06 hour, 07 hour, 08 hour, 09 hour, 10 hour, 11 hour…………….,22 hour, 23 hour
12hour format: 12 am, 1 am, 2 am, 3 am, 4 am, 5 am, 6 am, 7 am, 8 am, 9 am, 10am, 11 am, 12 pm, 1 pm, 2 pm………….9 pm, 10pm, 11pm.  In 12hour format, am stands for ‘anti meridiem’, which is Latin for ‘before midday’.
pm stands for ‘post meridiem’, which is Latin for ‘after midday’.  Comparison of 12hour and 24hour conventions of time.
 EXAMPLE 2: Write 1:23 pm in 24hour format. Write 4:56 hours in 12hour format.
SOLUTION:
If we add 12hours i.e. 12:00 to a 12hour format time (only pm. am will be same), then the result is in 24 hour format. Therefore, 1:23+12= 13:23 in 24hour format.
4:56 hours in 12hour format = 4:56 am
Note:
 The times in am in 12hour format will be equal to 24hour format.
 To convert pm into 24hour format, add 12:00 to the time given in pm.
 To convert a time greater than 12 in 24hour format, subtract 12 from it to obtain the same time in 12hour format
Practice these questions
Q1) Aryan started his homework at 1:23 pm. He finished at 2:34 pm. How long did he take to do his homework?
Q2) It takes 3 hours 45 minutes for Bani to reach the airport from her house. If she wants reach the airport by 10:00 am, what time should she leave her house?
Q3) A train travels from city A to city B. The train leaves at 05:06 pm. It takes 78 hours 19 minutes for the train to reach city B. When would the train arrive in city B?
Q4) It takes 2 hours 30 minutes for Chinmay to reach town B from town A. Today, he reached town B 45minutes later. How long did he take today to reach town B?
Q5) Write the elapsed time for the following start and end time.
Q6) Write down 6 hours 7 minutes 8 seconds in terms of minutes and seconds.
Q7) Write down the date of the next leap day in dd/mm/yyyy format.
Q8) How many days are there in between 9^{th} February, 2016 and 10^{th} March, 2016.
Q9) Add/Subtract 2 years 3 months and/from 4 years 10 months.
Q10) Write 5:01 pm and 6:07 am in 24hour format. Write 13:08 hours and 8 hours 9 minutes in 12hour format.
Recap
 When we convert higher units of time to its lower units, we multiply.
 When we convert lower units of time to its higher units, we divide.
 A leap year is a year which can be divided by 4.
 A leap year has 366 days instead of 365 days.
 In leap year, the extra day is added to the month of February. It has 29 days instead of 28 days.
 In AB:CD hours, AB is in the hours place and CD is in the minutes place.
 In 24hour format, the range is from 00 hours to 23 hours
 In 12hour format, there are two periods of 12 hours, each ranging from 1 am/pm to 12 am/pm
 Carry of 60 minutes in min position= Added as 1 hour in hours position
Borrow of 60 minutes is subtracted as 1 hour from hours position.