Vedic Mathematics: Secrets skills for quick, accurate mental calculations
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About this ebook
The step-by-step easy methods explained in this book help to remove the mathematics phobia commonly present in students and boost their self-confidence. The short techniques elevate the performance level of the students in any exam be it school, college or competitive examination.
Salient features:
Salient features:
† Simple & lucid language
† Diagrammatic and step-by-step explanation
† Solved examples for clear understanding
† Practice exercise & Word of caution in every chapter
† Time Saving Tricks & Shortcuts
† Mini Mathematics Refresher
† Brain racking puzzles
#v&spublishers
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Vedic Mathematics - EDITORIAL BOARD
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Preface
2012 is designated as National Year of Mathematics in India to mark the 125th birth anniversary of mathematical genius Srinivasa Ramanujan. Henceforth, his birthday 22nd December will be celebrated as National Mathematics Day in India. This book is an effort to commemorate the year of mathematics by highlighting the use of ancient vedic mathematical techniques in the modern world.
The main aim of the book is to remove the fear of mathematics and make it an enjoyable subject. The step-by-step explanation and the solved examples give a clear understanding of the various mathematical methods thereby increasing self-confidence. The word of caution in every chapter warns the students against common errors.
Taking the advantage of my long experience in teaching Mathematics my aim has been to showcase that acquiring skills in numbers can be easy, interesting, relevant and importantly super fun!
This book is a creation not only of the author but also of the editor, Mr. D J Borah as well as the wonderful designing and production team at V& S Publishers. The guidance from Mr. Sahil Gupta and encouragement from Mr. Vinod Gupta are incomparable. I sincerely thank them all for their valuable inputs.
As there is always a scope for improvement, any suggestion from my fellow teachers, students and other readers are most welcome.
– Sumita Bose
Tickle Your Brain
I. Playing Cards
A deck of cards is divided into three separate piles - A, B and C.
In pile A there are three times as many Blacks as there are Reds.
In pile B there are three times as many Reds as there are Blacks.
In pile C there two times as many Blacks as there are Reds.
How many cards of each colour are there in each of the three piles?
II. Population
Aryabhatta Nagar has two types of flats - Type I and Type II.
The number of people living in Type I flat is less than five hundred.
One third, one fourth, one fifth and one seventh of the population of Type I flats are all whole numbers. The sum of these fractions is equal to the ratio of the population living in Type II flats to that of the population of Type I flats. How many people live in Type II flats?
III. Waking Time
Mr. Ayush Ghosh catches a local train everyday from Howrah station. Unfortunately one day he fell asleep when the train still had twice as far to go as it had already travelled. Due to some unusual jerks he woke up halfway through the trip.
However, he fell asleep again. Now the train had half the distance to go that it had already covered. Mr.Ghosh woke up at the end of the journey.
What part of the total journey was he awake?
IV. Square Transformation
Suresh was given a 13 by 13 square sheet in an interview and asked to divide it into minimum number of squares. For example, the first square could be four by four the second five by five etc. He was also given the following conditions:
More than one square can be of the same size.
All the squares cannot be of the same size.
No portion of the big square can be left out.
Overlapping of squares is not allowed.
What was the least number of squares which Suresh could draw on the 13by 13 square sheet by fulfilling the above conditions?
V. Party Time
At a New Year party a person said - In this party there are 17 children, 12 males, 19 females and 14 adults. If you include me the number of different boy- girl couple would be equal to the number of different man-woman couple.
Is the speaker a boy, a girl, a man or a woman?
Playing Cards
Let the number of red cards be x or z and the number of black cards be y.
From the above table we get,
Red Cards: x + 3y + z = 26........................................................................................(1)
Black Cards: 3x + y + 2z = 26....................................................................................(2)
Multiplying equation (1) by 2 and subtracting it from equation (2) we get,
x – 5y = -26
Or, x = 5y - 26............................................................................................................(3)
Therefore, y cannot be less that 6 (otherwise 5y - 26 will not be positive).
Now, multiplying equation (1) by 3 and subtracting it from equation (2) we get,
– 8y - z = – 52
Or, z = 52 – 8y...........................................................................................................(4)
Therefore, y cannot be more than 6 (otherwise 52 – 8y will not be positive).
Thus, ify is neither more than 6 nor less than 6 then it must be equal to 6.
Substituting y = 6 in equation (3) and (4) we get x = 4 and z = 4. Hence,
In pile A there are 4 red cards and 12 black cards.
In pile B there are 18 red cards and 6 black cards.
In pile C there are 4 red cards and 8 black cards.
Population
The population of Type I flat is less than 500.
Moreover it is a number which has 3, 4, 5 and 7 as integral factors.
Since 3,4,5,7 are relatively prime therefore, LCM of 3,4,5,7 = 3 X 4 x 5 x 7 = 420 Thus, the population of Type I flat is 420.
Now,
Waking Time
When Mr. Ayush Ghosh fell asleep for the first time the train still had twice as far to go as it had already travelled. That means he fell asleep when the train had travelled one-third of the total distance.
He woke up half way through the trip.
Hence his sleeping time was,
When Mr.Ghosh fell asleep for the second time the train had half the distance to go that it had already covered. That means he fell asleep again at the two-third