Day 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 7 day clock 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 day arithmetic 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 day 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 7 day clock 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, if the divisor is 7, it is called as day clock
arithmetic. Since the divisor is 7, the remainders must be less than or
equal to 6. So, the remainder are 0,1,2,3,4,5,6. **

**"0" corresponds to "Sunday"**

**"1" corresponds to "Monday"**

**"2" corresponds to "Tuesday"**

**"3" corresponds to "Wednesday"**

**"4" corresponds to "Thursday"**

**"5" corresponds to "Friday"**

**"6" corresponds to "Saturday"**

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

1. A work was assigned to John on a Tuesday.He took 72 days to complete this work.On what day did he complete the work?

Tuesday corresponds to 2 in 7 day clock arithmetic.

We want to know the day which is 72 days after Tuesday.

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

Step1: Add 72 to 2

Step2: Divide the result by the divisor 7

Step3: Take the remainder

72 + 2 = 74

When 74 is divided by 7, the remainder is 4

4 corresponds to Thursday.

Hence, John completed the work on Thursday.

We want to know the day which is 72 days after Tuesday.

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

Step1: Add 72 to 2

Step2: Divide the result by the divisor 7

Step3: Take the remainder

72 + 2 = 74

When 74 is divided by 7, the remainder is 4

4 corresponds to Thursday.

Hence, John completed the work on Thursday.

2. What was the day 23 days before Monday?

Monday corresponds to 1 in 7 day clock arithmetic.

We want to know the day which is 23 days before Monday.

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

Step1: Subtract 23 from 1. That is, 1-23 = -22

Step2: Find the next integer after 22 which is exactly divisible by 7. That is 28.

Step3: Now -22 can be written as -22 = -28 + 6

6 corresponds to Saturday.

Hence, the day 23 days before Monday was Saturday.

We want to know the day which is 23 days before Monday.

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

Step1: Subtract 23 from 1. That is, 1-23 = -22

Step2: Find the next integer after 22 which is exactly divisible by 7. That is 28.

Step3: Now -22 can be written as -22 = -28 + 6

6 corresponds to Saturday.

Hence, the day 23 days before Monday was Saturday.

3. What will be the day 20 days after Monday?

Monday corresponds to 1 in 7 day clock arithmetic.

We want to know the day which is 20 days after Monday.

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

Step1: Add 20 to 1

Step2: Divide the result by the divisor 7

Step3: Take the remainder

20+1 = 21

When 21 is divided by 7, the remainder is 0.

0 corresponds to Sunday.

Hence, the day 20 days after Monday will be Sunday.

We want to know the day which is 20 days after Monday.

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

Step1: Add 20 to 1

Step2: Divide the result by the divisor 7

Step3: Take the remainder

20+1 = 21

When 21 is divided by 7, the remainder is 0.

0 corresponds to Sunday.

Hence, the day 20 days after Monday will be Sunday.

4. Michael was assigned a work on Thursday. He agreed to complete the work after 25 days. But he took two more days to complete the work. On what day did he complete the work?

Thursday corresponds to 4 in 7 day clock arithmetic.

We want to know the day which is (25+2=) 27 days after Thursday.

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

Step1: Add 27 to 4

Step2: Divide the result by the divisor 7

Step3: Take the remainder

27+4 = 31

When 31 is divided by 7, the remainder is 3.

3 corresponds to Wednesday.

Hence, Michael completed the work on Wednesday.

We want to know the day which is (25+2=) 27 days after Thursday.

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

Step1: Add 27 to 4

Step2: Divide the result by the divisor 7

Step3: Take the remainder

27+4 = 31

When 31 is divided by 7, the remainder is 3.

3 corresponds to Wednesday.

Hence, Michael completed the work on Wednesday.

5. Mr. Lenin's birthday was on Monday. He visited Newyork 28 days before his birthday. On what day, did he visit Newyork?

Lenin's birthday was on Monday. Monday corresponds to 1 in 7 day clock arithmetic

We want to know the day which was 28 days before Monday.

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

Step1: Subtract 28 from 1. That is, 1-28 = -27

Step2: Find the next integer after 27 which is exactly divisible by 7. That is 28.

Step3: Now -27 can be written as -27 = -28 + 1

1 corresponds to Monday.

Hence, Lenin visited Newyork on Monday.

We want to know the day which was 28 days before Monday.

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

Step1: Subtract 28 from 1. That is, 1-28 = -27

Step2: Find the next integer after 27 which is exactly divisible by 7. That is 28.

Step3: Now -27 can be written as -27 = -28 + 1

1 corresponds to Monday.

Hence, Lenin visited Newyork on Monday.

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