Month arithmetic is one of the sub topics of Modular Arithmetic which plays a major role in quantitative aptitude test. It is bit difficult to score marks in competitive exams without knowing the shortcuts related to month arithmetic, We have already learned this topic in our lower classes.Even though we have been already taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is,
we need to apply the appropriate short cut and solve the problems in a
limited time. This limited time will be one minute or less than one minute in most of
the competitive exams.

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Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today it is bit difficult to score marks in competitive exams without knowing to solve word problems on this topic. Whether a person is going to write placement exam to get placed or a student is going to write a competitive exam in order to get admission in university, they must be knowing the shortcuts related to month arithmetic, day clock arithmetic and hour clock arithmetic. This is the reason for why people must study this topic.

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

Students will learn, how and when they have to apply shortcuts to solve the problems which are related to this topic. Apart from the regular shortcuts, students can learn some additional tricks in this topic. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to solve the word problems on this topic which are being asked in competitive exams. The stuff which I have mentioned above is nothing but the tricks and shortcuts which need to solve the problems in a very short time.

Short cut is nothing but the easiest way to solve word problems on this topic month arithmetic. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

**BASIC CONCEPT**

**In
modular arithmetic, since there are 12 months in a year, it is the same as the 12 hour clock arithmetic . So, in month arithmetic, the divisor is 12. Since the divisor is 12, the remainders must be less than or
equal to 11. So, the remainder are 0,1,2,3,4,5,6,7,8,9,10,11 **

**"0" corresponds to the "December"**

**"1" corresponds to "January"**

**"2" corresponds to "February"**

**"3" corresponds to "March"**

**"4" corresponds to "April"**

**"5" corresponds to "May"**

**"6" corresponds to "June"**

**"7" corresponds to "July"**

**"8" corresponds to "August"**

**"9" corresponds to "September"**

**"10" corresponds to "October"**

**"11" corresponds to "****November**"

**Here,
we have some problems on month arithmetic. You can check your answer online and see step by
step solution.**

1. What month is 19 months after July?

July corresponds to 7 in month arithmetic

We want to know the month which is 19 months after July

To get answer for our question, we have to do the following steps.

Step1: Add 19 to 7

Step2: Divide the result by the divisor 12

Step3: Take the remainder

7 + 19 = 26

When 26 is divided by 12, the remainder is 2

2 corresponds to February

Hence, the month which is after 19 months will be February .

We want to know the month which is 19 months after July

To get answer for our question, we have to do the following steps.

Step1: Add 19 to 7

Step2: Divide the result by the divisor 12

Step3: Take the remainder

7 + 19 = 26

When 26 is divided by 12, the remainder is 2

2 corresponds to February

Hence, the month which is after 19 months will be February .

2. What month was 19 months before July?
?

July corresponds to 7 in month arithmetic

We want to the month which was 19 months before July.

To get answer for our question, we have to do the following steps.

Step1: Subtract 19 from 7. That is, 7-19 = -12

Step2: 12 is exactly is divisible by 12.

Step3: Now -12 can be written as -12 = -12 + 0

0 corresponds to December

Hence, the month 19 months before July was December.

We want to the month which was 19 months before July.

To get answer for our question, we have to do the following steps.

Step1: Subtract 19 from 7. That is, 7-19 = -12

Step2: 12 is exactly is divisible by 12.

Step3: Now -12 can be written as -12 = -12 + 0

0 corresponds to December

Hence, the month 19 months before July was December.

3. Anderson took a work in the month of September and agreed to completed the work after 17 months. In which month, did he complete the work?

September corresponds to 9 in month arithmetic

From the question, we want to know the month which is 17 months after September.

To get answer for our question, we have to do the following steps.

Step1: Add 17 to 9

Step2: Divide the result by the divisor 12

Step3: Take the remainder

9 + 17 = 26

When 26 is divided by 12, the remainder is 2

2 corresponds to February

Hence, Anderson completed the work in February.

From the question, we want to know the month which is 17 months after September.

To get answer for our question, we have to do the following steps.

Step1: Add 17 to 9

Step2: Divide the result by the divisor 12

Step3: Take the remainder

9 + 17 = 26

When 26 is divided by 12, the remainder is 2

2 corresponds to February

Hence, Anderson completed the work in February.

4. Jack started a work at in the month of June. He was given 38 months time to complete the work. But he took 3 months more to complete the work. In which month did he complete the work?

June corresponds to 6 in month arithmetic

From the question, we want to know the month (38+3=) 41 months after June.

To get answer for our question, we have to do the following steps.

Step1: Add 41 to 6

Step2: Divide the result by the divisor 12

Step3: Take the remainder

6 + 41 = 47

When 47 is divided by 12, the remainder is 11

11 corresponds to November

Hence, he completed the work in the month of November.

From the question, we want to know the month (38+3=) 41 months after June.

To get answer for our question, we have to do the following steps.

Step1: Add 41 to 6

Step2: Divide the result by the divisor 12

Step3: Take the remainder

6 + 41 = 47

When 47 is divided by 12, the remainder is 11

11 corresponds to November

Hence, he completed the work in the month of November.

5. Now the month is March. Johnson was in japan 45 months before. In which month, was Johnson in Japan?

March corresponds to 3

We want to know the month which was 45 months before march.

To get answer for our question, we have to do the following steps.

Step1: Subtract 45 from 3. That is, 3-45 = -42

Step2: Find the next integer after 42 which is exactly divisible by 12. That is 48.

Step3: Now -42 can be written as -42 = -48 + 6

6 corresponds to June

Hence, Mr. Johnson was in Japan in the month of June.

We want to know the month which was 45 months before march.

To get answer for our question, we have to do the following steps.

Step1: Subtract 45 from 3. That is, 3-45 = -42

Step2: Find the next integer after 42 which is exactly divisible by 12. That is 48.

Step3: Now -42 can be written as -42 = -48 + 6

6 corresponds to June

Hence, Mr. Johnson was in Japan in the month of June.

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