In modular arithmetic, if the divisor is 7, it is called as hour clock arithmetic.

Because 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"

**
**

**Case 1 :**

Let us say today is Friday. Find the day after 32 days from today.

"5" corresponds to "Friday"

If you want to find the day after 32 days from now, you have to add 32 to 5 and divide the result by 7.

5 + 32 = 37

When 37 is divided by 7, the remainder is 2.

"2" corresponds to "Tuesday"

So, the day after 32 days from now is Tuesday.

**Case 2 :**

Let us say today is Tuesday. Find the day after 4 days from today.

"2" corresponds to "Tuesday"

If you want to find the day after 4 days from now, you have to add 4 to 2 and divide the result by 7.

2 + 4 = 6

Here 6 is less than 7. So, we can not divide 6 by 7.

"6" corresponds to "Saturday"

So, the day after 4 days from now is Saturday.

**Case 3 :**

Let us say today is Saturday. Find the day before 32 days from today.

"6" corresponds to "Saturday"

Subtract 32 from 6.

6 - 32 = -26

Here, we get a negative value.

In the case of getting a negative value, we have to find the next integer which is exactly divisible by 7.

That is, we have to get the next integer after 26 which is exactly divisible by 7.

It is 28.

Now, we have to write -26 in terms of -28.

So, -26 can be written as

-26 = -28 + 2

"2" corresponds to "Tuesday"

Therefore, the day 32 days before was Tuesday.

**Problem 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 ?

**Solution :**

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.

**Step 1 :**

Add 72 to 2.

72 + 2 = 74

**Step 2 :**

Divide 74 by 7.

74/7

**Step 3 :**

Take the remainder, when 74 is divided by 7.

The remainder is 4.

"4" corresponds to "Thursday"

So, John completed the work on Thursday.

**Problem 2 :**

What will be the day 20 days after Monday ?

**Solution :**

**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. **

**Step 1 :**

**Add 20 to 1.**

**1 + 20 = 21**

**Step 2 :**

**Divide 21 by 7. **

**21/7**

**Step 3 :**

**Take the remainder, w****hen 21 is divided by 7. **

**The remainder is 0. **

"0" corresponds to "Sunday"

**So, the day 20 days after Monday will be Sunday.**

**Problem 3 :**

What was the day 23 days before Monday ?

**Solution :**

**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. **

**Step 1 :**

**Subtract 23 from 1.**

**1 - 23 = -22**

**Step 2 :**

**We get negative value in step 1 and also 22 is not divisible by 7.**

**So, find the next integer after 22 which is exactly divisible by 7. **

**That is 28. **

**Step 3 :**

Write -22 in terms of -28.

So, -22 can be written as

-22 = -28 + 6

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

**So, the day 23 days before Monday was Saturday.**

**Problem 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 ?

**Solution :**

**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. **

**Step 1 :**

**Add 27 to 4.**

**27 + 4 = 31**

**Step 2 :**

**Divide 31 by 7. **

**31/7**

**Step 3 :**

**Take the remainder, w****hen 31 is divided by 7.**

**The remainder is 3. **

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

**So, Michael completed the work on Wednesday.**

**Problem 5 :**

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

**Solution :**

**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. **

**Step 1 :**

**Subtract 28 from 1. **

**1 - 28 = -27 **

**Step 2 :**

**We get negative value in step 1 and 27 is not divisible by 7.**

**So, find the next integer after 27 which is exactly divisible by 7. **

**That is 28. **

**Step 3 :**

Write -27 in terms of -28.

So, -27 can be written as

-27 = -28 + 1

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

**So, Lenin visited Newyork on Monday.**

Apart from the stuff given above, if you need any other
stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**