Question

The sum of digits of a two digit number is 9 if 27 is subtracted from the number the digits are reversed find the number

Answer 1

Let the no. be x and y
x+y=9
10x + y -27=10y +x
9x-9y =27
x-y=3
Add both equations
We get 2x=12
x=6 and by putting this value whether in first or second equation we get y=3
Hence the number we get is 63.
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Answer 2

let the number be X and Y
therefore, the two digit number =10x+y
and reversed no. =10y+x
given :x+y=9. ------------1

also given
10x+y-27=10y+x
9x-9y=27
9(x-y) =27
x-y=3. -------2
adding 1 and 2
2x=12
x=6
therefore y=9-x =9-6=3
the two digit number=10x+y=10*6+3=60+3=63