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2015-03-08T04:32:43+08:00

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Let x be the tens digit
and y be the unit digit
 
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

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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.

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So if you want to be sure if it's right and you want to check it, here it is:
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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