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

Table of Contents

## 1. Squaring (Math Shortcuts)

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

For example – Find the square of 43.

= (43 + 3) × (43-3) + (3 × 3)

= (46 × 40) + 9

= (460 × 4) + 9

= 1840 + 9 = 1849

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

## 2. Multiplication

Vedic mathematics gave us the easiest method of complex multiplication. This method can be quickly explained with an example.

Multiply 62 with 32.

#### Multiply with 5

Just multiply the number by 10 and then divide it by 2.

For example 99 × 5 = 990/2 = 495

#### Multiply with 99

Multiply the number with 100 and then subtract the same number from the result. Let us take an example

Multiply 32 × 99 = 3200 – 32 = 3168

Also Read: Cool math games for kids

## 3. Mixture (Math Shortcuts)

Questions related to mixing can be easily solved by the obligation method. Using Mathematics, we can make a comprehensive arrangement of Mathematics questions. Let me explain this with a simple example.

Examples

Priced at $ 60 per liter of alcohol. If Samuel is selling water for $ 40 per liter. The profit margin remains the same. What is the ratio of water and alcohol in the mixture?

## 4. Square Root

**Square root of 4096:**

Here one’s digit is 6, so we will find that out of the numbers from 1 to 9, the space with 6 digits will have 6 and 6 digits. Therefore, either 4 or 6 will make a number of square marks. 4096.

⇒ Now we will find that in which class number from 1 to 9 is closest to the last two digits of 4096 i.e. 40 which will be 62 = 36. So 4096 out of 64 or 66 can be square root.

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

Also Read: Cool math games for kids

## 5. Cube Root (Math Shortcuts)

#### 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.

## 6. Quadratic Equations:

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

⇒ Here, product = x2 × coefficient of constant = 1 × 40 = 40

⇒ Add = (-1) × Coefficient x = (-1) × (-13) = 13.

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

⇒ Therefore, 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

Also Read: Cool math games for kids

## 7. Compound Interest

#### 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

#### 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

## 8. Time and Work (Math Shortcuts)

Each question in the Time and Work chapter can be easily solved by searching for the efficiency of the workers or subject (such as pipe).

For example – A takes 10 days to complete a job. BIt takes 20 days to complete the same work. If they work together in how many days will they complete the work?

⇒ A efficiency = 100/10 = 10% per day

⇒ B efficiency = 100/20 = 5% per day

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

## 9. 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

Also Read: Cool math games for kids

## 10. Number series (Math Shortcuts)

In number series questions, you need to find the pattern of the 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 exam.

## 11. Estimation (Math Shortcuts)

This is the most important technique. It is not a secret that every successful candidate is using this technique during the examination.

Example – 112 × 92

Just 112 × 9 = 1008

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

⇒ Answer 10304

You need to do all the calculations of your brain. Do not use paper. You need to divide complex calculations into parts and solve it without paper in your brain. In this way toppers make complex calculations during the exam.

It will be difficult for you to use this method right now, but with practice, you will be able to do any complex calculation within seconds.

## 12. Rule 72, 114 and 142

The 72 rule is a shortcut technique that will estimate the number of years it takes your money to double with compound interest.

For example: If you pay Rs. 100, how long will it take to double your money, if the rate of interest is 6%?

So, 72:

72 according to the rule of 6 i.e. 12 years.