Percentage equivalents

The following table could be helpul in reducing our calculations.




Memorize the above table so that it can be used during calculations which would reduce the time considerably.

For example if you have to multiply 150 X 6.66%
you can just use 1/15 in place of 6.66%
ie , 150X(1/15) = 10

Like this you can switch between percents ,decimals and fractions to calculate faster.

Speed conversions

The basic formula to convert from km/h to m/s is

value * 1000 m/3600 sec)
ie , value * 5/18

For converting m/s to km/h, it is

value * 3600 sec/1000 m)
ie , value * 18/5

Example for converting 60 km/h to m/s

60*5/18 = 16.66 m/s

Temparature conversions

Converting Fahrenheit (F)to Celsius (C)

(F - 32) x 5/9 = C
a)subtract 32
b)mulitply by 5
c)divide by 9


Shortcut for coverting Celcius to Fahrenheit.
(C x 1.8) + 32 = F
(C x 2) - (C x 2 x 0.1) + 32 = F

a) double the Celsius temperature
b) subtract 10% of the doubled temperature
c) add 32

Adding Time

Here is a cool trick I learnt today to add hours and minutes together:

Let's try adding 2 hr and 23 minutes and 3 hr 46 minutes together.

Make the 2 hr 23 minutes into one number, which will give us 223 and do
the same for the other number, 3 hours 46 minutes, giving us 346

Now add these two numbers together:

223
346
___
569

So we now have a total of 569.

No matter what the hours and minutes are,just add the 40 time constant to the total.

569 + 40 = 609

Now split the number to get our answer is 6 hrs and 09 minutes!

Converting Kilometres to Miles

This is a useful method for convert kilometres to miles .

The formula to convert kilometres to miles is number of (kilometres / 8 ) X 5

So lets try 160 kilometres into miles

160/8 = 20

multiplied by 5 is 100 miles!

Another example lets try 120 KM

120/8=15
15*5 =75

thats it 75 miles.

Converting Kilos to Pounds

In GMAT unit conversions are more important and we need to do it correctly and swiftly here is a tip for converting Kilos to Pounds.

20 kilos into pounds:

Step one: multiply the kilos by TWO.

21 x 2 = 42

Step two: divide the answer by ten.
Just put a decimal point one place in from the right.

42 / 10 = 4.2

Step three: add two step answers.

42 + 4.2 = 46.2

And thats the answer

21 kilos = 46.2 pounds

CI

We all know the traditional formula to compute interest...
CI = P*(1+R/100)^N - P

The calculation get very tedious when N>2 (more than 2 years). The method suggested below is easier way to get CI/Amount after 'N' years.

You need to recall the Pascal's Triange which wold look like this:




Example: P = 1000, R=10 %, and N=3 years. What is CI & Amount?

Now Amount after 3 years = 1 * 1000 + 3 * (10% of 1000) + 3 * (10% of 100) + 1 * 1*(10% of 10) = Rs.1331/-
The coefficents - 1,3,3,1 are taken from the pascal's triangle where n=3.

 
CI after 3 years = 3*100 + 3*10 + 3*1 = Rs.331/- (leaving out first term in prevoius step)

If N =2, we would have had, Amt = 1 * 1000 + 2 * 100 + 1 * 10 = Rs. 1210/-
CI = 2 * 100 + 1* 10 = Rs. 210/-

This method is extendable for any 'N' and it avoids calculations involving higher powers on 'N' altogether!

VEDIC MATHS:Trick to Multiply numbers between 11-19

Now you must be having a doubt will it work for bigger numbers ?

yes it will only difference is you need to do carry over as you do in normal multiplication.

Example:

234X13
1) add zero in front of 234  ------------- 0234X13
2) the digit in units place of 13 is 3 and digit sucessive to 4{right most) is zero as there is nothing.
The value comes to 12 so put 2 and carry over 1

So do the following (4X3)+0 =12           0234X13
                                            1                 
                                              2
Now move towards left ,next digit is (3X3)+4 =13
add the carry over 1 + 13 =14                 0234X11
                                               1       
                                                42
Now move towards left ,next digit is (2X3)+3 =9      0234X13
add the carry over 1 + 9 =10                         1 
                                                       042
Now move towards left ,next digit is (0X3)+2 =2      0234X13
add the carry over 1 + 2 =3                          3042

Cleared???

VEDIC MATHS :Trick to Multiply numbers between 11-19

Here are the Rules :
1) prefix the number to be multiplied by zero .
2)The figures in the answer is obtained by adding the units place of number (11-19) with the each figure of the number to be multiplied and adding the sucessive number to it.(this shuold be done similar to our multiplication from right to left)


Example:

234X11
1) add zero in front of 234  ------------- 0234X11
2) the digit in units place of 11 is one and digit sucessive to 4{right most) is zero 

So do the following (4X1)+0 = 4           0234X11
                                             4
Now move towards left ,next digit is (3X1)+4 =7      0234X11
                                                       74
Now move towards left ,next digit is (2X1)+3 =5      0234X11
                                                      574
Now move towards left ,next digit is (0X1)+2 =2      0234X11
                                                     2574

Isnt it easy and cool?

VEDIC MATHS Multiplication by 5^n

You have to just add n number of zeros to the right of the number to be muliplied and divide it by number formed by 2^n

example 987654 X 125 = 987654 X 5^3
= 987654000 / 2^3
= 987654000 / 8
= 123456750

VEDIC MATHS :Distributive law of multiplication

Distributive law of multiplication over addition: ( m + n ) · k = m · k + n · k

59876X9999 = 59876 X (10000-1)

= 598760000 - 59876

= 598700124

VEDIC MATHS :Multiplying by sixteen

First, multiply the number in question by 10. Then multiply half the number by 10. Then add those two results together with the number itself to get your final answer.

For example: 16 × 24
Step 1: 24 × 10 = 240
Step 2: (24 × 1/2) × 10 = 12 × 10 = 120
Step 3: add steps 1 and 2 and the number = 240 + 120 + 24 = 384

VEDIC MATHS :Multiplying by thirteen

Put the tens digit on the left, the unit number on the right, add them up together in the middle. Then add double the number to the previous result.

For example: 13 × 22
Step 1: (2 × 100) + 2 + [(2 + 2) × 10] = 242.
Step 2: 22 × 2 = 44.
Answer: 242 + 44 = 286.

If the two digits sum to more than ten, then you carry the one to add it to the number on the left and continue.

For example: 13 × 65
Step 1: (6 × 100) + 5 + [(6 + 5) × 10] = 715.
Step 2: 65 × 2 = 130.
Answer: 715 + 130 = 845.

VEDIC MATHS :squares of numbers from 50 to 59

To find the squares of numbers from 50 to 59
For 5X^2 , use the formulae
(5X)^2 = 5^2 +X / X^2
E.g. (55^2) = 25+5 /25
=3025
(56)^2 = 25+6/36
=3136
(59)^2 = 25+9/81
=3481

VEDIC MATHS :squares of numbers

To find the squares of numbers near numbers of which squares are known
To find 41^2 :
Add 40+41 to 1600 =1600+81
=1681
To find 59^2 :
Subtract 60^2-(60+59) =3600-119
=3481

To find the number of factors of a given number

To find the number of factors of a given number, express the number as a product of powers of prime numbers.

In this case, 48 can be written as 16 * 3 = (24 * 3)

Now, increment the power of each of the prime numbers by 1 and multiply the result.

In this case it will be (4 + 1)*(1 + 1) = 5 * 2 = 10 (the power of 2 is 4 and the power of 3 is 1)

Therefore, there will 10 factors including 1 and 48. Excluding, these two numbers, you will have 10 – 2 = 8 factors.

VEDIC MATHS :Numbers with same first digits

Multiply two numbers with same first digits and sum of second digit numbers is ten.
If you want to multiply two numbers like 47 x 43 then
(4 x 5) | (7x3) = 20|21 = 2021
We are multiplying the common first digit number with one number more ie , 4 with 5 in this case and concatenating the last digits multiplied with this.

VEDIC MATHS :Multiplication Easier

Here are some tricks to make multipliacation easier .
Every one will be comfortable when they multiply with a single digit numbers and similarly with division.
So we can use the following technique to make your multiplication simpler.

Multiply by 5 -you can just add a zero at the end of the number and divide it by 2.
156 x 5 --------> 1560/2 -------- > 780
Multiply by 25 –you can add two zeros at end and divide it by 4.
156 x 25 ------------> 15600/4 ---------> 3900
Multiply by 75 – You can multiply by 300 and divide by 4.
156 x 75 ------------->156x300/4 ----------->46800 /4 -------->11700
Similarly
Multiplying with 45 = number x90/2
Multiplying with 125= number x500/4
Multiplying with 225= number x900/4
Multiplying with 275= number x1100/4