Today I am going to summarise all the maths tricks that will speed up your calculation speed. I used them for CAT and IBPS exams. I am sure that these tricks will help you increase your score. I have written many articles in detail on these topics. Click on respective links to get details.

## Squaring

In this simple trick, we need to modify the equation and make the units digit zero. After all, it is easy to multiply when units digit is zero.

= (43+3) × (43-3) + (3×3)**For example - Find square of 43**=(46×40) + 9

= (460×4) + 9

= 1840 + 9 = 1849

### Finding Square of Any No. From 1 to 100

Read my full post on Squaring trick,

## Multiplication

Vedic maths gave us the easiest method to do complex multiplications quickly. This method can be quickly explained with an example.Multiply 62 with 32

**Step 1**

**Step 2**

**Step 3**

Detailed post on Multiplication technique (Multiplication of 3 digit numbers)

Read quick Multiplication technique without using complicated Vedic maths

### Multiplication with 5

Simply multiply the number by 10 and then divide it by 2.For example 99×5= 990/2= 495

### Multiplication with 99

Multiply the number with 100 and then minus the same number from the result. Let's take an exampleMultiply 32×99 = 3200 - 32 = 3168

## Mixture

Questions related to mixtures can be easily solved by alligation method. By using alligation we can wide arrange of maths questions. Let me explain this with a simple example

Example

The price of wine of $60 per litre. If Samuel is adding water with and selling the mixture for $40 per litre. Profit margin remains same. What is the ratio of water and wine in the mixture?

Detailed post on Alligation method (Application on various types of questions)

Example

The price of wine of $60 per litre. If Samuel is adding water with and selling the mixture for $40 per litre. Profit margin remains same. What is the ratio of water and wine in the mixture?

## Square Root:

#### Square root of 4096:

Here the one's digit is having 6, so we will find square of which numbers from 1 to 9 are having 6 in the ones digit place which will be 4 and 6. So either 4 or 6 will form the one's digit of the square root of 4096.⇒ Now we will find square of which number from 1 to 9 is the closest to the last two digits of 4096 i.e. 40 which will be 62 = 36. So either 64 or 66 can be the square root of 4096.

⇒ Now multiply this 6 with its next number 7 which will come as 42. As 40 is smaller than 42, hence the smaller number 64 will be the desired square root.

## Cube Root:

#### Cube Root of 19683:

⇒ Here the one's digit is having 3, so we will find cube of which numbers from 1 to 9 are having 3 in the ones digit place which will be 7. So 7 will form the one's digit of the cube root of 19683.⇒ Now 19 falls between the cube of 2 and 3, so the smaller number between 2 and 3 i.e. 2 will form the tens digit of the cube root.

⇒ Hence, the cube root of 19683 will be 27.

==>> Learn Cube Root quick trick here

## Quadratic Equations:

####
a) x^{2}-13x+40=0:

⇒ Here, Product = Coefficient of x2 × constant = 1 × 40=40⇒ Add = (-1) × Coefficient of x = (-1) × (-13)= 13.

⇒ If the product is positive, the sign of the roots will be same and it will depend upon the sign of the Add. So in this case, the sign of the roots will be positive.

⇒ Hence, x = 8, 5

####
b) x^{2}-x-6=0:

⇒ Here, Product = Coefficient of x2 constant = 1×(-6) = -6⇒ Add = (-1)×Coefficient of x = (-1)×(-1) = 1

⇒ If the product is negative, the sign of the roots will be different and the sign of the bigger root will be similar to the sign of the Add and the sign of the smaller root will be the complementary. So in this case, the sign of the bigger root, 3 will be positive and the smaller root, 2 will be negative.

⇒ Hence, x = 3, -2

==>> Read Quadratic Equations shortcuts here

## Compound Interest:

####
a) C.I. for 2 years, CI_{2} = R_{2}% × Principal where, R_{2}=2r|r^{2}

**Example**: Principal = 10,000; Rate = 12%; Time = 2years

Here, R2 = 2×12|12×12 = 24|144 = 25. 44

⇒ CI2 = 25.44% × 10000 = 2544

####
b) C.I. for 3 years, CI3 = R_{3}% × Principal where, R_{3}=3r|3r^{2}|r^{3}

**Example**: Principal = 25,000; Rate = 12%; Time = 3years

Here, R3 = 3×12|3×12×12|123 = 36|432|1728 = 40.4928

⇒ CI3 = 40.4928% × 25000 = 10123.20

## Time and Work

Every question in time and work chapter can be solved easily by finding the efficiency of workers or subject (such as pipes).**For example**- A takes 10 days to complete a job. B takes 20 days to complete the same job. In how many days they will complete the job if they work together?

⇒ A's efficiency = 100/10 = 10% per day

⇒ B's efficiency = 100/20 = 5% per days

⇒ A and B can do 15% of the work in a day if they work together. So they can do the whole job in 100/15 = 6.66 days or 6 days and 18 hours.

⇒ Detailed post on Time and Work chapter (Practice questions)

25% of Cost Price (1/4 of CP) = 20% of Selling Price (1/5 of SP)

Similarly, 1/3 of CP = 1/2 of SP

25% of Selling Price (1/4 of SP) = 20% of Cost Price (1/5 of CP)

Similarly, 1/3 of SP = 1/2 of CP

Profit and loss practice questions

Let's take an example :

Every consecutive difference is multiplied by -2.

Similar questions are asked in the exams.

Simply 112 × 9 = 1008

⇒ Add a zero 10080 and then add 224 to 10080.

⇒ Answer is 10304

You need to do all the calculations in your brain. Don't use paper. You need to divide complex calculations into parts and solve it in your brain without paper. That's how toppers do complex calculations during exams.

Right now it will be difficult for you to use this method but with practice, you will be able to do any complicated calculation within seconds.

## Profit and Loss

**Profit/loss = Sales price - Cost price**

**In case of profit**25% of Cost Price (1/4 of CP) = 20% of Selling Price (1/5 of SP)

Similarly, 1/3 of CP = 1/2 of SP

**In case of loss**25% of Selling Price (1/4 of SP) = 20% of Cost Price (1/5 of CP)

Similarly, 1/3 of SP = 1/2 of CP

Profit and loss practice questions

## Number Series

In Number series questions, you need to find the pattern of series.Let's take an example :

**16, 26, 6, 46, -34, ?**

**There is a pattern in the difference between the numbers in the series.**

Every consecutive difference is multiplied by -2.

Similar questions are asked in the exams.

## Estimation

That's the most important technique. This is not a secret that every successful candidate is using this technique during exams.**Example**- 112 × 92Simply 112 × 9 = 1008

⇒ Add a zero 10080 and then add 224 to 10080.

⇒ Answer is 10304

You need to do all the calculations in your brain. Don't use paper. You need to divide complex calculations into parts and solve it in your brain without paper. That's how toppers do complex calculations during exams.

Right now it will be difficult for you to use this method but with practice, you will be able to do any complicated calculation within seconds.

## Rule of 72, 114 and 142

The rule of 72 is a shortcut technique to estimate the number of years it will take for your money to double with compounding interest.For example: If you are invested Rs. 100, then how much time it will take to double your money, If the rate of interest is 6%?

So, according to rule of 72:

72 ÷ 6 i.e. 12 years.

Read the complete post on Rule of 72, 114 and 144 here

## Linear Equations

This technique has been originated from Vedic Maths. This technique will### Example

### Step 1 - Find Numerator

Cross multiply the coefficient of y with independent terms.

### Step 2 - Find Denominator

The denominator is obtained by cross multiplying (4 ✖️ 2) and subtracting from it the cross product of (5 ✖️ -3) as shown below:-

### Value of x

**For more Concepts and Tricks Click here**

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we need to modify the equation and make the units digit zero. After all it is easy to multiply when units digit is zero.

ReplyDeleteSir I want to know that these techniques u hv given are they from the book magical book on quicker maths????cause the techniques of solving problems using mix n alligatn is very good...kindly reply.....

ReplyDelete66*66 solve by this method.

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Delete3 man or 04 women complete a work in 43 days . 07 man or 05 women complete in how many days

ReplyDeleteplease short cut method

use the chain rule. you will gate the answer in seconds

Delete17 mamu 17

DeleteAns will be 12 days.

DeleteSir I need more examples on finding square root of a number.Thank you sir for your valuable suggestions and tricks :)

ReplyDeletehi,i m lekha gonna final year i couldnt understand dis square root method if u know means can u pls explain it to me clearly dear

Deletepercentage chain rule can give quick results

ReplyDeleteany trick for 17*23

ReplyDeleteSir can u pls post the tricks of percentage, profit-loss & partnership??

ReplyDelete@Ramandeep .. Please add SBI PO MAINS TEST SERIES IN TESTPANDA

ReplyDeleteIT IS SHOWING THE PRELI EXAM Only. also add RBI aSSISTANT EXAM

Please explain question no. 8

ReplyDeleteThe sum of two numbers is 2000 and their L.C.M. Is 21879. The two numbers are?

ReplyDelete1989,11

ReplyDeleteHow to solve this?? Full solution

ReplyDeleteWe add shortly

ReplyDeleteLet the two no. be " x " & "(2000-x)".

ReplyDeleteNote that, 21879 & 2000 are co-primes, so x & (2000-x) are also co-primes..., this means HCF is 1.

Now u can calculate the value of "x" as,

x (2000-x) = 21879 * 1 ( since d product of HCF & LCM = d product of no.s)

x= 11, 1989

Thanks :)

ReplyDelete8th Ans is 35( C option ) as per my knowledge. Can anybody explain how come option D.

ReplyDeleteYes i think ur right option c as 35must be the answer as becoz we get same remainder as 7from each division

ReplyDeleteSir, I know this website is totally dedicated only for banking aspirants but I want to clear bank as well as SSC CGL this year. So plz sir it is my heartiest request provide some notes specially for math viz. Geometry, trigonometry and quadatric equations. Plz sir it is more helpful for SSC aspirants

ReplyDeletesir., answer to qn no. 8 is option c ( 35 )

ReplyDeleteif u look at the common differences:

147 - 77 = 70

252 - 147 = 105

You want the greatest common factor of 70 and 105, which is 35

The solutions gives confusion.. So I just asked.. My ans is 35..

ReplyDeletetyping error! Option c is right

ReplyDeletetypo error! option c is right!edited now

ReplyDeletetypo error! edited now!c is right

ReplyDeletetypo error!

ReplyDeleteI will try

ReplyDeletethanku very much :)

ReplyDeletethanks

ReplyDeleteI will try

ReplyDelete