Question

sum of two digit of a two digit number is 9 when we interchange change the digit it is found that the resulting new number is greater than the original number by 27 what is two digit number ​

Answer 1

Answer:

Let the digits at tens place and ones place: x and 9−x respectively.

∴ original number =10x+(9−x)

=9x+9

Now Interchange the digits: Digit at ones place and tens place: x and 9−x respectively.

∴ New number: 10(9−x)+x

=90−10x+x

=90−9x

AS per the question

New number = Original number +27

90−9x=9x+9+27

90−9x=9x+36

18x=54

x=  

18

54

​  

 

x=3

Digit at tens place ⇒3 and one's place : 6

∴ Two digit number: 36

Answer 2

Answer :

The required number is 36

Given :

• The Sum of the digits of a two digit number is 9
• When we interchange the digits it is found that the resulting new number is greater than the original number by 27.

To Find :

• The original number

Solution :

Let us consider the digits be x and y respectively

Therefore, the number is :

10x + y

According to Question :

Firstly The Sum of the digits of a two digit number is 9.

$\sf{x + y = 9........(1)}$

and secondly when we interchange the digits it is found that the resulting new number is greater than the original number by 27.

$\sf10y + x = 10x + y = 27 \\ \\ \sf \implies10y - y + x - 10x = 27 \\ \\ \sf \implies9y - 9x= 27 \\ \\ \sf \implies9(y - x) = 27 \\ \\ \sf \implies y - x= 3............(2)$

Adding the equations (1) and (2) :

$\sf \implies \: x + y + y - x = 9 + 3 \\ \\ \sf \implies2y = 12 \\ \\ \bf \implies y = 6$

Now putting the value of y in (1) :

$\sf \implies x + 6 = 9 \\ \\ \implies \sf x = 9 - 6 \\ \\ \bf \implies x = 3$

Thus , the original number is :

$\sf \longrightarrow10 \times 3 + 6 \\ \\ \sf \longrightarrow30 + 6 \\ \\ \bf\longrightarrow36$