Number of Poles in a Fence
A farmer built a fence around his 17 cows, in a square shaped region. He used 27 fence poles on each side of the square.
How many poles did he need altogether?
A Steamer’s Route
A 150 metre long steamer has changed its direction through 30 degrees while moving through a distance equal to twice its own length. Can you tell the radius in the circle in which it moves?
Absolute Value
Supposing the roots of quadratic equation are:
8/5 and -7/3
What is the absolute value of the coefficient of the x term, if the equation is written in standard form (ax2 + bx + c = 0), and a = 1
Name of the Exchange
In Great Britain some years back the first three letters of a telephone number used to indicate the name of exchange. How many such arrangements of 3 letters is it possible to devise from the 26 letters of the alphabet?
A Game of Billiards
Rajiv, Sanjiv and Vijay were playing a game of billiards. Rajiv can give Sanjiv 10 points in 50, and Sanjiv can give Vijay 10 points in 50. How many points in 50 must Rajiv give Sajiv to make an even game?
Counting A Billion
If you were to count one number per second and counted seven hours per day, how long would it take you to count to a Billion?
Checking of Calculations: Casting Out Nines
While doing arithmetic calculations, we should normally check our calculation. But the checking should not be as tedious as the original problem. To solve this problem I am explaining below a very frequently used method which is discussed in Vedic Mathematics as well as by many other mathematicians.
Vedic Sutra: Vedic Mathematics Technique
Beejank: The Sum of the digits of a number is called Beejank. If the addition is a two digit number, then these two digits are also to be added up to get a single digit.
Find the Beejank of 632174.
As above we have to follow
632174 --> 6 + 3 + 2 + 1 + 7 + 4 --> 23 --> 2 + 3 --> 5
But a quick look gives 6 & 3 ; 2 & 7 are to be ignored because 6+3=9,2+7=9.
Hence remaining 1 + 4 --> 5 is the beejank of 632174.
Checking of Addition
Thumb Rule: Whatever we do to the number, we also do to their digit sum: then the result we get from the digit sum of the number must be equal to the digit sum of the answer.
For example: The number: 12+45+96+75+25 =253
The digit sum = 3+9+6+3+7 =28=10=1
Answer’s digit sum: 2+5+3 =10=1 (verified)
Another example: 3.5+23.4+17.5 = 44.4
The digit sum: 8+9+13=8+9+4=21=3
Answer’s digit sum: 12=3 (verified)
Casting Out Nines
This method is also known as "casting-out-nines". The method involves converting each number into its "casting-out-nines" equivalent, and then redoing the arithmetic. The casting-out-nines answer should equal the casting-out-nines version of the original answer. Below are examples for using casting out nines to check addition.
We get the casting-out-nines equivalent of a number by adding up its digits, and then adding up those digits, until you get a one digit number. If our answer is 9, then that becomes 0. As a short cut, we don't have to add in any of the 9's in our work, as these are the equivalent of 0. We can just "cast out" those 9's. For example, 19 becomes 1, without even adding 1 and 9 and getting 10, and then adding 1 and 0 and getting 1. As a further short cut, we can group numbers together which add up to 9, and replace them with 0. 2974 becomes 4, because we can cast out the 9 and the 2+7 (which is also 9 or 0). Well, let's try an arithmetic problem:
137892 3
+ 92743 + 7
------ --
230635 1
3+7=10, casting out 9 we get 1.
This rule is also applicable to subtraction, multiplication and up to some extent to division also
In the next post I will explain the use of this method for all of them.
Third Dimension of Box
I have a box. The two dimensions of the box are 4” and 3”. Compute the third dimension of the box so that the space diagonal of the box is and integer.
Why Front Wheels Wear Out?
Perhaps you have noticed the wheels of some carts - the front ones are smaller than the rear ones. Why do the front axles wear out faster than the rear?
Abra Cadabra
SEVEN VIGINTILLION, THREE HUNDRED FORTY SIX NOVEMDECILLION, SIX HUNDRED FORTY EIGHT OCTODECILLION, FOUR SEPTEDECILLION, FIVE HUNDRED SIXTY SEXDECILLION, NINE HUNDRED EIGHTYSIX QUINDECILLION, TWO HUNDRED FIFTEEN QUATTOUR DECILLION, THREE HUNDRED FORTY EIGHT DUODECILLION, FOUR HUNDRED FORTY FOUR UNDECILLION. TWO HUNDRED EIGHTYSIX DECILLION, FOUR HUNDRED FORTY FIVE NONILLION, THREE HUNDRED AND FIVE OCTILLION, ONE HUNDRED FORTY SIX SEPTILLION, THIRTY NINE SEXTILLION, ONE HUNDRED FORTY QUINTILLION, FORTY SIX QUADRILLION, NINE HUNDRED SIXTY TRILLION, SIX HUNDRED SEVENTY EIGHT BILLION, FIVE HUNDRED EIGHTYTWO MILLION, TWO HUNDRED FIFTY SIX THOUSAND AND THREE. Can you write this as a numeral?
Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
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Recent Comments
1.3 2. yes 3.he could get out after 30 days if he would be alive... – 18May12
Really thanks .... hats of you ... please tell me such a important tricks of... – 18May12
Very nice – 16May12
Hey, i think the question ll be like : A and B separately can do... – 13May12
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