Question

sum of the digits of a two digit number is 9 when we interchange the digit it is found that the resulting new number is greater than the original number by27 what is the original number

Answer 1

let the ones digit be x
and tens digit be y

According to question,

y + x = 9

10x + y = 10y + x + 27

9(x - y) = 27

x - y = 3
x + y = 9
2x = 12

x = 6

6 - y = 3

y = 3

number = 63

Answer 2

Hey dear


Here your answer

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Suppose that number is xy


So, 10x+y= xy


Here given that x & y sum is 9

So..

x+y= 9


Now we interchange this number

It is greater than 27 to old number


New number is

yx= 10y + x


10y+ x is greater than 27 to 10x+ y


So

27+10x+y= 10y+x

9x-9y+27=0

x-y= - 3


We solve to (x+y=9) & (x-y= - 3)


x+y=9

x-y=-3
_______

2x= 6

x= 3

& y= 6

So. Ur answer is 36


Hope it helpful