# The sum of the digits of a two digit number is 9.if the digits of the numbers are reversed the new number is decreased by 9.find the number

Let the number will be 10x+y

So

sum of digits = 9
x + y = 9
x = 9-y

if digits are reversed, the new number will be 10y+x

And according to the question

(10x+y) - 9 = 10y+x
10x + y - 9 - 10y - x = 0
10x - x + y - 10y - 9 = 0
9x - 9y - 9 = 0
9(x - y - 1) = 0
x - y - 1 = 0   (use x = 9-y)
9 - y - y - 1 = 0
-2y + 8 = 0
2y = 8
y = 4
x = 9-y = 9-4 = 5
The number is 10x+y = 10×5+4 = 54

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