HOW TO ROUGHLY CHECK YOUR INCOME TAX STATEMENT

DIGIT SUM: We should know first, what is digit sum?
Take 81245. Add all digits.
8+1+2+4+5 = 20 Again add 2+0 = 2. Hence 2 is the digit sum of 81245. By repeatedly adding digits; till we reach a single digit, we get digit - sum.

Note : In a number, we can ignore 'nines' and the digits which add up to nine. They will not have any effect on the calculation of digit-sum.

For example; in 7295, 7,2 and 9 can be ignored, and the digit-sum is just 5.
In usual method 7+2+9+5 =23=2+3=5, Also we get 5.

To verify multiplication
7195*4321 = 31089595
Find the digit-sum of each of the above numbers
4 * 1 = 4
Hence verified. So the rule is; 'The digit-sum of the multiplicand when multiplied with the digit-sum of the multiplier should equal to the digit-sum of the product'.

TO VERIFY DIVISION
5046/42 = 120; REMINDER 6 , WE KNOW 5046 = 120*42 +6
DIVIDEND = DIVISOR * QUOTIENT + REMINDER
Now we will use digit-sums and verify.
6 = 3* 6+ 6
AGAIN DIGIT- SUM
6 = 6 checked.

Next addition,
3475+9892 + 7461 = 20828 using digit sum
1 + 1 + 9 = 2
2 = 2
it is Ok.

Similarly, we can verify squaring, square root, cube, cube rooting.
" When the sum-digits does not match, we can say the answer is 100 % wrong."

But when the sum_digits matches, the answer is mostly correct and NOT 100% CORRECT. We have to employ a few more techniques to confirm the answers.

1. 7212 *3982, these two numbers can be taken as 7000 and 4000. Hence the answer should be around 28000000.
2. The answer should have eight digits.
3. The last digit of the answers must be 4 (2*2 =4)
Intuitively, we can employ techniques like this and check the answers.

The rough and fast checking is useful for students giving competitive exams; the executives verifying 'typo' in a balance sheet; etc.,
This method belongs to vedic mathematics
-------------------------------------------------------------------------------------------------.

Comments

LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

sciencecapsules

Search This Blog