# Sum of the Two Digits of a Number is 9. When We Interchange the Digits the New Number is 27 Greater Than the Earlier Number. Find the Number

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The number is 36.

Now we have to find the required number:

Given that, sum of the two digits of a number is 9

Consider xy as the number which can be represented as 10x + y

x + y = 9

x = 9 – y

When the digits are swapped, the new number is 27 more than the old one.

The new number is yx once the digits are exchanged.

From the question,

(10y + x) – (10x + y) = 27

9y – 9x = 27

y – x = 27/9

y – x = 3

As x + y = 9

y – (9 – y) = 3

y – 9 + y = 3

2y = 3 + 9

On simplifying we get

y = 12/2

y = 6

As x = 9 – y

x = 9 – 6

x = 3

So we get

xy = 36

### History of Digits

Roman abacuses or stone tokens were employed thousands of years ago when people were not familiar with the numerical system. The need for larger denominations was recognised as time passed and trade between nations and regions advanced. The development of number systems as we know them today was a result of this. The need to deal with larger numbers also emerged as the nations advanced. The size of a bacterium, the distance between the earth and the moon, and other wonders inspired us to develop larger number systems. As a result, the idea of numbers and digits was introduced.

Summary:-

## Sum of the Two Digits of a Number is 9. When We Interchange the Digits the New Number is 27 Greater Than the Earlier Number. Find the Number

Sum of the two digits of a number is 9. When we interchange the digits the new number is 27 greater than the earlier number. The number is 36. The operations on numbers are used to find the solution.

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