<PRE><B>Question 615680</B>
Let x be the tens digit
and y be the unit digit
 
So,

10x + y =  number
The sum of the digits of a number is 9.
x + y = 9............(1)

Reversing the digits decrease the number by 9.
10y + x = 10x + y - 9
10y - y = 10x - x - 9
9y = 9x - 9
9y = 9(x - 1)
Divide above equation by 9, we have 
y = x - 1
y-x=-1..............(2)


Add (1) and (2)

y - x = -1
x + y = 9
--------------          
2y=8.........(2)

Divide by 2 both sides
2y/2=8/2
y = 4
Put the value of x in (1)
x+y=9
x+4=9
x=9-4
x=5

Digits are 5 and 4
and number is 54


Check
======
The sum of the digits of a number is 9
5+4=9
9=9

Reversing the digits decrease the number by 9.
45=54-9
45=45

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