G.S.T( Goods and Services Tax)

 Before 1 July 2017, We have VAT ( Value Added Tax) system. But After 1 July 2017 we have a new Tax System called G.S.T( Goods and services tax ).Because our page is purely dedicated to Mathematics so, we only talk about Mathematics behind the term G.S.T. Here I am not going deep conversation of G.S.T that this system is good or bad? More clearly , Today we only discuss how to calculate G.S.T. Before going Mathematically, Here I am giving some terminology which is needed to understand G.S.T and its concept. "One Nation one tax" this is the main theme behind  concept of G.S.T. Some basic terminology are as follows:-

1) There are three types of G.S.T 

          (a) C.G.S.T ( Central Goods and Services Tax)

          (b) S.G.S.T ( State Goods and Services Tax) 

          (c) I.G.S.T( Integrated Goods and Services Tax)

2) Intra  State Transactions:- 

When the location of the supplier and the place of supply are in the same state then this type of transactions are called Intra State Transaction.

2) Inter State Transactions:- 

when the location of the supplier and the place of supply are not in the same state then this type of transactions are called Inter State Transaction.

Here is some concepts related to calculation of G.S.T.

   (I)  When there is a intra state transactions the Tax is equally divided between the state government and central government.

  ( II) When there is a inter state transactions then I.G.S.T is calculated and this Tax is collected by central government and the central government decide how to distribute this tax between the states.

  (III) When we calculate C.G.S.T and S.G.S.T in intra state transactions the tax is equals to half of the G.S.T.

 

After all these background, let start some interesting Mathematics.

Firstly , To be honest if you know how to calculate percentage then you definitely able to understand the concepts and also calculate G.S.T easily but if.........................

 

We understand G.S.T by some examples because there is no formula in calculation of G.S.T.

Q.) Find the amount of bill of the intra state transaction of good of cost 250 and G.S.T is 12%. 

Ans: In this question it is clearly mentioned that the transaction is intra state.We have to calculate C.G.S.T and S.G.S.T.we also known that C.G.S.T and S.G.S.T  is equal to half of G.S.T 

      i.e., C.G.S.T=S.G.S.T = (G.S.T)/2 = 6% 

now you known better than me what we have to do next .

           S.G.S.T = 250*6/100=15

  and C.G.S.T= 15

so, total bill =250+15+15=280.

Second type of G.S.T calculation is when a whole seller B take some goods from manufacturer A and whole seller give it to consumer or a small shopkeeper C .

 

In this type of transaction first G.S.T is calculated when A sell to B and second G.S.T is calculated when B sell to C .But now Question is, What amount of G.S.T is paid by B?

Simply, B is to pay

              G.S.T =( G.S.T collected at second transaction) - (G.S.T paid at first transaction)

This is because when A buys goods from the manufacturer, he paid G.S.T and when he sell this item to C ,he again paid a G.S.T collect from C. which is  not seems fair. So, he paid 

    G.S.T =( G.S.T collected at the time of selling ) - ( G.S.T paid at the time of buy).

Now after reading the above discussion you definitely talk about G.S.T with anyone with no fear and also you are able to calculate G.S.T. And one more thing if you know  the basic mathematics of class 8th you definitely able to calculate the G.S.T. 

Thank you

S.K Ojha 

The Sequence of Chapters In Content Of Any Book.

 Every book have a definite content. And every book have a definite aim behind the content. The writers of the books want to express their way of thinking about that subject or topic. May this happen that your way of thinking of reading that  book is different from though of  writer. But if you wanted to understand the concept behind the sequence of chapters and what is the aim of a book then  You have to read book according to sequence of chapters. This topic came in my mind when my teacher start teaching me with chapter number three. I am really confused that why not from the chapter 1st. But , Now I got the answer. Teacher wanted teach easy thing first. In mathematics, nothing is hard and nothing is easy but it is depend upon your concepts. In Mathematics, it is very important to follow the sequence of content at least one time because every chapter is connected with each other. It may possible that Book is divided in sections but trust me these sections also have some important connections and this way of reading books is justice with the writer of that book, justice with the aim of book. Here, I am taking my first example for explaining my thought more clearly. For this example I used the content of NCERT  Mathematics book for the class 11th. The sequence given in this book is as follows:

1) Sets 

2) Relations and functions

3) Trigonometric functions

4) Principle of Mathematical Induction

5) Complex Numbers and Quadratic Equation

6) Linear inequalities

7) Permutations ad combinations

8) Binomial Theorem

9) Sequence and series

10) Straight line 

12) Introduction to three dimensional Geometry 

13) Limits and Derivatives

14) Mathematical Reasoning

15)Statistics

16) Probability 

Appendix:

 Infinite series:

                * Introduction

                * Binomial theorem for any Index

               *  Infinite Geometric series

                * Exponential series Logarithmic series

Mathematical Modeling:

            * Introduction 

            * Preliminaries 

           * What is Mathematical Modeling 

You can also see the photo of the content:

When I saw this content at this stage, I clearly saw that writer want develop a basic understanding of  Mathematics and wanted that the student become familiar with Mathematics in higher educations and one more thing that the sequence of the chapters is essential because Sets are used in chapter Relations and functions and with this concepts students are ready to read a special type of function named trigonometric functions and similarly other chapter are also connected with each other . Even though Appendix is very interesting and relatable with my point of view.

Now I am taking a my second example of NCERT book of history for class 10th.The name of this book is India and Contemporary world II. sequence of chapters in this book is as follows:

1) The Rise of Nationalism in Europe 

2) Nationalism in India

3) The making of a Global world 

4) The age of Industrialization

5) Print culture and the modern world.

This book also have many purpose. One thing is to give a understanding that any incident happens in the world may also have an impact on India. Another concept is to study comparatively and many more concepts that this book wanted to teach us. Now it depend on us that what we thinking about that book while reading. What is our aim to study that book. And students who understand this then it become a bless for them  and a teacher need to explain these concepts and teach students with this concepts and if teacher found a new concept related to that book then teacher need to explain that concept.

"Take a good book to bed with you - books do not snore"                 ---George R.R. Martin

Thank you.

S.K. Ojha 

Did You Know These Facts About Average Of Numbers

 

In our classes teacher teaches us that average of n number is given as

And this is only about average. But this is not fare with average concept. Here, I give you some basic understanding and some concept related to numbers.

First thing I cleared here that average is a tool which help us to see a broader picture of many problem or solution .Some key words that you must here in your daily life that average internet connection speed, Average income of a family, etc.

Wikipedia said that an average is a single number taken as representative of a list of numbers.

This is a different view of seeing average beside of its formulae. With the help of average you can say many things about its entries which are used in average. I know these things are not in your books but you have to think these things to yourself. And here I give you a way how to think?

Take a example, if average of 10 numbers is 1 then what you can say about these ten numbers. What that 10 number be? For this come on the mathematical form.

         

=   a1+a2+a3+………..+a10 = 10

From above it is clear that the sum of that 10 numbers is 10, if average is 1. If entry is whole number then a1, a2, a3 ………, a10 ≤ 10. Which means that entries lies between 1 to 10. Not only this, but you can say more about these entries. If a single number is equals to 10 then all other are necessarily equals 0. Similarly, if a entry is equals to 5 then other all entries are less then or equals to 5. Similarly, for other possibilities.

Now the last but not the least, What is the basic difference between Average and Arithmetic mean. This question arises here because average of two numbers is 

 and Arithmetic mean is same. Then what is difference between them?

Arithmetic mean is only defined for special kind of progression called Arithmetic progression in which difference between any two consecutive entries is same.

So, if a₁ ,a₂ , a₃ ,…..a_n  are in Arithmetic progression then arithmetic mean of a₁ and a₃ gives a₂ and arithmetic mean is calculated only when the series is  in Arithmetic progression. But Average is calculated for ant number and no need of any special progression.

Many more concepts are hidden inside the formulae and definition.Some of them are written in books and some of them you have to think your self.

Thank you.

S.K. Ojha

Mathematics of Geometry

Many students, incliding me, never talk about geometry in the class of algebra but now I realize that the right way of study of algebra is to connect it with geometry . It is impossible to explain all Algebra with geometry here. So, Today I give you only a way of thinking.One thing that I always quote that Geometry is extremity of every mathematics or every mathematics have their use in Geometry. So, here I give you a list of topics Whose geometry is very Interesting. I think you must have a pen and copy. 

1)Algebra: 

This branch of mathematics have many uses and always have a geometry. If you get a topic in algebra whose geometry is known then its your turn to discover that. We always write many equation like x=0, y=o or x-y=0 ,x^2-y^2=1 etc. 

All these type of equations have definite geometry in Cartesian plan or Euclidean space. Some of above equation are represents a line, some represents curves and and many other eqations are there in Algebra which give you a solid geometry in 3-D.Also we very often use the term "find the root " as:

*what is the root of x^2=1 or x^4=1 ( In real plan and in complex plan). 

*what is the root of the system of equation

                             x-y=1

                            X-2y=2

Try these questions without calculations. ( Hint : Use geometry) 

2) Vector calculus:-

I strictly recommend you that vector calculus is always with geometry becuase this is frequently used in geometry and in engineering, Some examples are as follows: 

 Dot product of two vector:

With the use of  dot product you can find the angle between them since 

                

Dot product has the geometry interpretation as the length of the projection of x onto the unit vector of y when the two vectors are placed so that their tails coincide.

Similarly, there are many terms as cross product, divergence, gradient, curl, etc,. have a geometry Interpretation. 

As we saw two topics whose geometric interpretation is quite interesting. Similary, differential equations are used in geometric problems ,diffrential calculus, trigonometry, integrations, etc have a geometric use. For undergraduate students Groups also have a geometric interpretation and extremity of Groups and rings are called Algebraic geometry. This post may be a trouble for your teachers beacuse now they have to explain more in their classes. But if teacher denies to explain all your question ,never stop yourself and mail me your doubt I will try my best to explain you. 

🙏🙏Thanks🙏🙏

S. K. Ojha

Discovery of a sub atomic particle Pi Masons: Dr. Bibha Chowdhuri

 *This article is dedicated to the unknown or we can say that known by only few of us, Bibha Chowdhuri. And this article is a question for all of us.*

*Why this name is not known to everyone ?*

*Is this great scientist not deserves the noble prize..?*

*This question is for all of us.*.

I am going to start the introduction of this lady scientist by a recent incident : An unsung brilliant Indian scientist,Bibha chowdhuri,was honoured by the International Astronomical Union by naming a white yellow dwarf star after her name. The star ‘Bibha’ is 340 light years away in the constellation of Sextans.

Bibha Chowdhuri worked at Tata Institute of Fundamental Reserch for 8 years. She worked with Homi J. Bhabha and Vikram Sarabhai. And she also worked with Noble prize winner and great physicist P. M. S. Blacket(Google this name for more)  

And now why I am saying this lady deserve a Noble Prize. Bibha Chowdhuri  discovered the pi-meson, a subatomic particle, in Darjeeling before the independence of India. 

And a book is writen on her work, named "A Jewel Unearthed :Bibha Chowdhuri".

I can't introduce this lady but after reading the above lines you can easily think about her greatness in her field. But my question is still same why this lady is unknown to many of us ? And the biggest question why not Noble Prize to her? For this you have to read and research on the history. What are the factors working behind all these stuff ? Beside of all this question, we are also,intellectual class of the nation, was responsible for all these things. why she didn't get her fame despite this great discovery. If we are using the internet in the right way. And if Indian parents support their children to go in higher education then definitely they came to know about names like Vibha Chowdhuri. Here I took only one example of Bibha Chowdhuri but there are many more names of great ones whose name is unknown to us and they have disappeared in the pages of history.I am quoting here that "Talente is hidden till to be viral".

Thanks

Shivam kumar ojha

BOOK: IN MY WAY

 May you think that this topic is out of our mission towards subjects.But trust me, read this post, you will get your answer. 

If you are going to buy a new book please don't be too fast in buying the book. Many people have this behaviour that whenever they see a book, with nice name and cover, they directly buy that book. Believe me, this way of buying books decrease the value of book. 

Now, if you are not of this type then this post is for you. India's Great scientist and former President (Lt) Dr. A. P. J Abdul Kalam said that "A good book is equal to thousand friends while a good friend is equal to a library. "This quotation is absolutely right. But Here I am going to talk something different about this quotation. No doubt, a good friend is equal to a library but careful and read again this statement. Here Kalam Sahab talking about a good friend. And finding a good friend is really near to impossible. But finding a good book comparatively easy. So, buy a good book which is equal to thausand friends. 

Now, the question is How you know that which book is good? This task is also not hard but you can do it if you stop yourself for a while.

If here I explain each and every line then this post beacome to long so try to read between the lines.

At first, the book you want to buy, must aquire some information about the content and also go through the comparative format. You should google it and also search the best books on the same topic and compare every book. No matter writer is so good or famous. You should buy that book which has a great content, concept, morality and a simple language. Try to read minimum two to three book on the same topic. Because the content of the book depends on the purpose for which it is written and always consult with your teacher and others. And after that you will be definitely able to buy a good book equal to thausand friends and this book give you a new way of thinking, new concepts and will take you on a trip to world tour.

Thankyou 

S.k.Ojha.

Special thanks to my Dear friend Govind Tripathi. 

How Mathematics changed our life?

This question is questioned by one of my far friend Pooja. Thank for giving me this new topic. I tried my best to explain this topic in simple and interesting way in this post.

     

      Since, this question is quite simple and interesting. And answer is depend on your connection with Mathematics. So, let's start this topic from the beginning of Mathematics. 

     If you are my reader and read my blogs then by definition of mathematics it give a simple way for solving and explaining the hard topics of different subjects. So, Mathematics is lifeline of every subjects.

        

         If you want to know how mathematics changed my life. So,  Mathematics is my religion and Mathematics is a holly book as The Bhagwat Geeta for me. Because, The Bhagwat Geeta gives answer of every question arises in your life and solve the problems of your life. Similary, If you think Mathematics, beside of calculations and many big theories, as a Religious book then you can get solutions of your life's problem in a Mathematical form. Now, let explore the Mathematics which changed the life of every people of every era. 

1) Vedic Mathematics:-

   This is a Mathematics of numbers which made you faster in calculation. This Mathematics gives very easy ways to calculate big calculations. If you love Mathematics then you must use this for calculations And this tipical form of Mathematics Changed the life of Ancient human. This Mathematics is alive right now and give birth to many other fields of mathematics.

2)Probability Theory:-

    This field of Mathematics is totally inspired by experience and humans enthusiasm to know what event is may happen in near future. What is probability of happening a event? This Field gives answer of many questions as

1) Can this happen that any astroide or metriods hit the earth and life on earth is extinct? 

 2)What is the probability of existence of life in universe? 

3)Probability of finding a electron around the neucleous.

And many more question which helps human to make life easy of human beings. 

In every era, of human existence, Mathematics always helps human to do something miraculous and With the help of mathematics ancient human made some monuments which is a wonder for today's human. 

Finally, I tell you honestly that this topic is really very vast and whole book can be written on this topic. So, I sum up this topic here. Mathematics is like a weapon for a warrior, Mathematics is a language for science.

Mathematics is always change his form only for helps people and to make life easy of human being. 

Thankyou

       

  Shivam kumar ojha