# 12 HOUR CLOCK ARITHMETIC

## About the topic 12 hour clock arithmetic

12 hour clock 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.

## Why is this topic needed?

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.

## What is the advantage of 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

## How can students apply shortcuts in modular arithmetic?

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.

## Shortcuts we use to solve the problems

Short cut is nothing but the easiest way to solve word problems on this topic 12 hour 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 12, it is called as 12 hour clock arithmetic. 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 hour "12"

"1" corresponds to the hour "1"

"2" corresponds to the hour "2"

"3" corresponds to the hour "3"

"4" corresponds to the hour "4"

"5" corresponds to the hour "5"

"6" corresponds to the hour "6"

"7" corresponds to the hour "7"

"8" corresponds to the hour "8"

"9" corresponds to the hour "9"

"10" corresponds to the hour "10"

"11" corresponds to the hour "11"

Here, we have some problems on 12 hour clock arithmetic. You can check your answer online and see step by step solution.

1. It is 9 hours now in a 12 hour clock. What will be the time after 18 hours.

 (A) 1 hour (B) 2 hours (C) 3 hours (D) 4 hours

jQuery UI Accordion - Default functionality
Now, the time is 9 hours. We want to know the time after 18 hours.

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

Step2: Divide the result by the divisor 12
Step3: Take the remainder

9 + 18 = 27

When 27 is divided by 12, the remainder is 3

Hence, the time after 18 hours will be 3 hours.

2. If the time now in a 12 hour clock is  is 9 hours, what was the time 71 hours back?

 (A) 7 hours (B) 8 hours (C) 9 hours (D) 10 hours

jQuery UI Accordion - Default functionality
Now, the time is 9 hours. We want to know the time 71 hours back.

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

Step1: Subtract 71 from 9. That is, 9-71 = -62
Step2: Find the next integer after 62 which is exactly divisible by 12. That is 72.
Step3: Now -62 can be written as -62 = -72 + 10

Hence, the time 71 hours back was 10 hours.

3. Lily was assigned a work when the time was 7 hours in a 12 hours clock. She completed the work after 72 hours. At what time did she complete the work?

 (A) 7 hours (B) 8 hours (C) 9 hours (D) 10 hours

jQuery UI Accordion - Default functionality
From the question, we want to know the time 72 hours after 7 hours.

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

Step2: Divide the result by the divisor 12
Step3: Take the remainder

7 + 72 = 79

When 79 is divided by 12, the remainder is 7

Hence, the time after 72 hours will be 7 hours.

4. Mr. Johnson started a work at 4 hours in a 12 hours clock. He was given 38 hours time to complete the work. But he took 3 hours more to complete the work. At what time did he complete the work.

 (A) 8 hours (B) 9 hours (C) 10 hours (D) 11 hours

jQuery UI Accordion - Default functionality
From the question, we want to know the time (38+3=) 41 hours after 4 hours.

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

Step2: Divide the result by the divisor 12
Step3: Take the remainder

4 + 41 = 45

When 45 is divided by 12, the remainder is 9

Hence, he completed the work at 9 hours.

5. Now the time is 6 hours and Mr. Lenin is at home. Lenin was in  Washington 81 hours before. At what time was he in Washington ?

 (A) 7 hours (B) 8 hours (C) 9 hours (D) 10 hours

jQuery UI Accordion - Default functionality
Now, the time is 6 hours. We want to know the time 81 hours before.

To get answer for our question, we have to do the following steps.
Step1: Subtract 81 from 6. That is, 6-81 = -75 Step2: Find the next integer after 75 which is exactly divisible by 12. That is 84. Step3: Now -75 can be written as -75 = -84 + 9

Hence, Mr. Lenin was in Washington at 9 hours.