# 10 Fast Maths Tricks and Shortcuts

Today I am going to summarise all the maths tricks that will speed up your calculation speed. I used them in CAT and IBPS exam. 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.

## List of Cool Maths Tricks

### 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.

For example - Find square of 43
= (43+3) × (43-3) + (3×3)
=(46×40) + 9
= (460×4) + 9
= 1840 + 9 = 1849

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 example
Multiply 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)

### To Find Square Root of a Number:

#### 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.

### To Find Cube Root of a Number:

#### 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.

### Solving Quadratic Equations for solving Inequality problems:

#### a) x2-13x+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) x2-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

### 5. Computing Compound Interest:

#### a) C.I. for 2 years, CI2 = R2% × Principal where, R2=2r|r2

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 = R3% × Principal where, R3=3r|3r2|r3

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)

### 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 × 92
Simply 112 × 9 = 1008

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.
Smart Prep Kit for Banking Exams by Ramandeep Singh - Download here

### Oliveboard Test Series(Recommended)

#### Bank Exams Today Notes

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

2. Sir 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.....

3. 66*66 solve by this method.

1. yep ho jata hai bhi

4. 3 man or 04 women complete a work in 43 days . 07 man or 05 women complete in how many days

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

2. Ans will be 12 days.

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

1. hi,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

6. percentage chain rule can give quick results

7. any trick for 17*23

8. Sir can u pls post the tricks of percentage, profit-loss & partnership??

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

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

10. Please explain question no. 8

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

12. 1989,11

13. How to solve this?? Full solution

15. Let the two no. be " x " & "(2000-x)".
Note 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

16. Thanks :)

17. Ajay GangannavarJuly 2, 2015 at 8:08 PM

8th Ans is 35( C option ) as per my knowledge. Can anybody explain how come option D.

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

19. Sir, 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

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

if 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

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

22. typing error! Option c is right

23. typo error! option c is right!edited now

24. typo error! edited now!c is right

25. thanku very much :)

26. thanks

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