What is Arithmetic

Arithmetic is the oldest and most elementary branch of mathematics. It is used by everyone to carry on with their day-to-day operations. Higher up it is used for scientific and business calculations. Arithmetic is to mathematics what letter is to a word. Arithmetic is the basic foundation of mathematics.

The two basic arithmetic operations are addition (+) and subtraction (-).  In its simplest form, addition combines two numbers into one. Subtraction finds the difference between two numbers. The difference can be either, positive, negative or zero.

From addition we can derive another operation called multiplication (× or *), which is nothing but repeated addition of the same number to another.

From subtraction we can derive another operation called division (÷ or /), which is nothing but repeated subtraction of the same number from another.

Arithmetic clears the logical thinking ability of our brain and makes it more and more analytical in its thinking prowess. Logic is concerned with the principles of correct reasoning, and it is the study of arithmetic which vastly improves our reasoning ability. 

A student, in his/her infancy, begins his/her study of mathematics with positive numbers and arithmetic. Arithmetic deals with natural numbers, integers, fractions, and decimals, which the student learns in course of time. In later stages a student learns how to solve basic problems using the various tools provided by arithmetic and logic. 

Arithmetic - A few important concepts about motion

A moving train starts crossing a post, a tree, a pillar, a standing man or any object of negligible length/width when the front part of the train meets the object.

The crossing ends when the end or rear part of the train just leaves the post or pillar or whatever.

A moving train starts crossing a bridge, a platform or any object, whose length/width can be determined, when the front part of the train just meets the beginning of the bridge or platform.

 The crossing ends when the end or rear part of the train just leaves the end of the bridge or platform or whatever object of determinable length.

Thus, to cross a post, a pillar, a tree or a standing man, a train will have to travel a distance equal to its own length.

Again, to cross a platform, a bridge or any object whose length/width can be determined, a train will have to cover a distance equal to the sum of its own length and the length of the bridge or platform. 

Problem: A train travelling at a speed of 72 km per hour passes a man standing on a platform in 18 seconds. The train passes the platform in 30 seconds. Find the length of the train and that of the platform.

Solution: According to the rule, in 18 seconds the train covers a distance equal to its own length as it takes 18 seconds to pass the standing man.
In 1 hour or 60 minutes the train covers 72 km.
Therefore, in 1 minute the train covers 72/60 km.
So, in 1 second the train covers 72/60 ÷ 60 km  = 72/60 x 1/60 km
So, in 18 seconds the train covers 72/60 x 1/60 x 18 km = 0.36 km = (0.36  x 1000) metres = 360 metres.

Therefore, the length of the train is 360 metres.

Again, in 18 seconds the train travels 360 metres.
So, in 1 second the train travels 360/18 metres.
Therefore, in 30 seconds the train travels 360/18 x 30 metres = 600 metres.

According to the rule, in 30 seconds the train travels a distance equal to the sum of its own length and that of the platform. This sum is 600 metres.

Now to get the length of the platform we have to subtract the length of the train from the sum. 
Therefore, the length of the platform is (600 - 360) metres = 240 metres.