# Advance Vedic Maths Digital Sum

Digital sum means adding digits of any group of numbers. It is also known as C9 method and Magic with 9 method.

Simply we need to add every digit of any big numbers, irrespective of point, percentage etc in between the numbers like 234.56 or 56%.

This technique is very useful for the students giving competitive exams as they are already provided four choices to every answer.

The digital sum technique is also very useful to check answers involving multiplication, division, addition, squares, square roots, cube roots etc.

The procedure of this method is very simple, only we have to convert any given number into a single digit by repetitive adding of all the digits of that number. e.g. digital sum of 23456 is 2+3+4+5+6 = 20

Sometimes the digit sum has more than one digit. Then you have to repeat this process until the digit sum is a single digit. We have called this single digit the Vedic digit for the number. e.g

234567 = 2+3+4+5+6 = 26 = 2+6 = 8

## Rules of Digital Sum

Rule 1: When a number is multiply by 9, it’s digital sum always be 9, e.g.

9 × 2 = 18 = 8 + 1 = 9
9 × 150 = 1350 = 1 + 3 + 5 + 0 = 9

Rule 2: When 9 is added to a number, it’s sum doesn’t change, so you need to cancel out 9 to calculate its digital sum, e.g.

First case: 12397536 = 1+2+3+9+7+5+3+6 = 36 = 3+6=9

Second case: 1 2 3 9 7 5 3 6 = 5 + 3 + 1 = 9
— Answer is the same, how?

• Cancel 9, cancel 7 and 2 (7+2=9), cancel 6 and 3 (6+3=9)
So when we cancel 9, 7, 3, 6 then only 5, 3, 1 remains, when we add 5, 3, and 1 it gives 9, which is the same as the first case.

Therefore if we cancel all these numbers as per the rule, our work becomes easier, so why waste unnecessary time when results are the same in both cases.

Rule 3: If a number gives 9 as its overall sum, it will be considered as 9, but it doesn’t happen in case of multiplication, e.g.
—- 6 + 3 = 9
—- 3 × 3 = 9- wrong as per rule

Rule 4: There is no impact of percentage and decimal on the sum of a number. e.g.
— 2.557 = 2 + 5 + 5 + 7 = 17 = 1 + 7 = 8
— 20% of 30 = 20 × 30 = 6 — how?
—————– = 20/100 × 30
—————– = 2 × 3 = 6

Rule 5: In a fraction if we have any number whose sum is not 1, then we have to make it 1. e.g. 5/1, 4/1, 6/1, 7/1 etc.

Example : In case of 2 / 5 we have to convert 5 to 1. i.e,
2/5 = 2×2 / 5×2 = 4/10 = 4/ 1+0= 4/1
4/7 = 4×4 / 7×4 =16/28 = 6+1/8+2=7/1+0=7/1

Rule 6: A number cannot be a perfect square if it’s digital sum is other than 1, 4, 7, 9

Rule 7: It is not used in case of approximation. e.g. when answe comes in decimals.

Rule 8: Whenever we get a negative (-ve) remainder, we will have to make it positive by adding 9 to the original.

## Application of Digital Sum

Question 1:

What is the sum of 41 + 23?
64 (b) 65 ( c) 67 (d) 56 ?

Solution: 41 + 23 = 4+1+2+3 = 10 = 1 + 0 = 1

64 = 6+4 = 10 = 1+0 = 1 ✔
65 = 6+5 = 11 = 1+1 = 2 ❌
67 = 6+7 = 13 = 1+3 = 4 ❌
56 = 5+6 = 11 = 1+1 = 2 ❌

Question 2:

What is the sum of 43751 + 53433 + 25653 + 2567 + 342?
i) 107746 ii) 107846 iii) 106646 iv) 107546

Solution:
—- 43751 + 53433 + 25653 + 2567 + 342
—— 2 + 0 + 3 + 2 + 0 = 7

i) 107746 = 1+0+7+7+4+6 = 25 = 2+5 = 7✔
ii) 107846 = 1+0+7+8+4+6 = 26 = 2+6 = 8❌
iii)106646 = 1+0+6+6+4+6 = 23 = 2+3 = 5❌
iv)107546 = 1+0+7+5+4+6 = 23 = 2+3 = 5❌

Question 3:

What is the sum of
4368 + 2158 + 596 – x = 1262 + 3421 ?

i) 1066 ii) 1177 iii) 1247 iv) 1384

Solution:

—- 4368 + 2158 – 596 – x = 1262 + 3421
——- 3 + 7 – 2 – x = 2 + 1
——- 8 – x = 3
——- -x = 3-8
—— x = 5

i) 1066 = 1+0+6+6 = 13 = 3+1 = 4 ❌
ii) 1177 = 1+1+7×7 = 16 = 1+6 = 7 ❌
iii) 1247 = 1+2+4+7 = 14 = 1+4 = 5 ✔
iv) 1384 = 1+3+8+4 = 16 = 1+6 = 7 ❌

Click Here To Learn Vedic Maths Subtraction

Question 4:

What is the digital sum of
408 × 3058 / 9452 = ?

i) 134 ii) 176 iii) 132 iv) 133

Solution:

— 408 × 3058 / 9452 = ?
— 3 × 7 / 2 = ?
— 21 / 2
— 3 / 2 = ?
— 1.5 = 1 + 5
— 6

i) 134 = 1+3+4 = 8 ❌
ii) 176 = 1+7+6 = 5 ❌
iii) 132 = 1+3+2 = 6 ✔
iv) 133 = 1+3+3 = 7 ❌

Question 5:

What is the sum of 258762 / 303?

i) 854 ii) 954 iii) 804 iv) 824

Solution:

— 258762 / 303 = 21 / 6 = 7 / 2
–7/2-As per Rule five you have to make it 1
— 7×5 / 2×5 = 35 / 10 = 8/10 = 8

i) 854 = 8+5+4 = 17 = 1+7 = 8 ✔
ii) 954 = 9+5+4 = 18 = 1+8 = 9 ❌
iii) 804 = 8+0+4 = 12 = 1+2 = 3 ❌
iv) 824 = 8+2+4 = 14 = 1+4 = 5 ❌

Question 6:

Which of the following is not a perfect square?

i) 354025 ii) 617796 iii) 15876 iv) 179876

Solution: Remember perfect square is only possible if the digital sum of any number is 1, 4, 7, 9.

i) 354025 = 1+9 = 10 = 1 ❌
ii) 617796 = 2+7 = 9 ❌
iii) 15876 = 2+7 = 9 ❌
iv) 179876 = 2+9 = 11= 2 ✔

Click Here to Learn Vedic Maths Square & Square Root

Question 7: (19)³

i) 6859 ii) 6159 iii) 4259 iv) 7329

(19)³ = 1 + 9 = 10 = 1 +0 = 1

i) 6859 = 19 = 1 ✔
ii) 6159 = 21 = 3 ❌
iii) 4259 = 20 = 2 ❌
iv) 7329 = 21 = 3 ❌

Question 8:
What is the digital sum of
30% of 420 – 56% of 350 = x – 94

i) 48.2 ii) 49.2 iii) 39.2 iv) 59.8

Solution:

30% of 420 – 56% of 350 = x – 94
9 × 6 – 2 × 8 = x – 4
-16 = x – 4
-7 = x – 4
X = – 3

Apply Rule number 8

X = – 3 + 9 = 6

i) 48.2 = 14 = 5
ii) 49.2 = 6 ✔
iii) 39.2 = 5
iv) 59.8 = 14 = 5

## Frequently Asked Questions

Q1. What is digital sum method?

Answer: Digital sum means adding digits of any group of numbers. It is also known as C9 method and Magic with 9 method.
Simply we need to add every digit of any big numbers, irrespective of point, percentage etc in between the numbers like 234.56 or 56%.

Q2. Where is digital sum used?

Answer: This technique is very useful for the students giving competitive exams as they are already provided four choices to every answer.

Final Word

From the above article you have learned a new concept of digital sum. We hope this method will help you in your competitive exam, where you can solve this kind of question fast by applying advanced vedic maths digital sum. Just remember rule number 7 and don’t apply this method there.