Question

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

Answer 1

let 
ones digit=x
tens digit=y
then the no=10y+x
the interchanged no= 10x+y
case 1
the sum of the digits is 9
x+y=9                 (eq 1)
case 2
the no is interchanged if subtracted by 27
10y+x-27=10x+y
10y-y+x-10x+27
9y-9x=27
by dividing both sides by 9
y-x=3                   (eq 2)
from eq 1 and 2 by elimination method (if u want the steps of this u can ask me)
we get y=6 and x=3
therefore as we know that the no is 10y+x
the no is 63
for verification 63-27=36 and hence the no is interchanged or 6+3=9 is the sum of the digits