Question

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 . What is the two digit number ?

Answer 1

Heya !

☆ here is your answer ☆

let original number=10x+y

Reverse number = x+10y

Case :1

let the sum of the two digit number be
x +y =9----(1)

Case : 2

x+10y = 10x+y + 27
10y - y = 10x - x + 27
9y= 9x + 27
9y - 9x =27---(2)

substituting (1) and (2)

x +y = 9 -- (multiply by 9)

9x-9y=27
_______
9x +9y= 81
9x-9y=27
(-) (+) (-)
________
= 》 18y=54
=》 y= 6

9x+9y=81
9x+9(6) =81
9x+54=81
9x=81- 54
9x= 27
x=27/9
x=3

Therefore no: 63

Hope this helps you ^_^

Answer 2

Hope u like my process
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Let the two digits be x and y and in such a way that

The original number is (10x + y)

And it seems like xy where x is in ten's place and y in one's place.

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Given
=-=-=-=-

=> x + y = 9 _______(1)

Again..

=> Interchanging the digits we get the number

= x +10y

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According to the problem
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
=> (10y +x) - (10x +y) = 27

=> 10y +x-10x - y =27

=> 9y - 9x = 27

=> 9(y - x) = 9×3

=> y - x =3 ______(2)

______________________
Adding equation (1) and (2) we get
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
$= > \\ \: \: \: \: \: \: \: \: \: \: y + x= 9 \\ \: \: \: + \: \: \: y - x = 3 \\ ................................ \\ = > 2y \: \: \: = \: \: 12 \\ \\ = > \bf \: y = \it \: \frac{12}{2} = \bf \underline6 \\ \\ = > \bf \: x = \it9 - y = 9 - 6 = \bf \underline 3$

___________________________
So the original number is (10x+y)

= (3×10) +6 = 36

Which is in xy form.

______________________
Hope this is ur required answer

Proud to help you