Question

Sum of the digits of a two digit number is 11. The given number is less than
the number obtained by interchanging the digits by 9. Find the number.

Answer 1

let the tens digit be x and units digit be y x+y=11-------eq2
1ox+y=1oy+x-9
9x-9y=-9
x-y=-1-----------------eq 1

adding both equations
2x=10
x=5
substituting value of x
x-y=-1
5-y=-1
y=6
number 56

Answer 2

Two digit number: xy= 10x+y.

Sum of digits: x+y=11

xy is less then yx by 9: xy+9=yx 

xy+9=yx

10x+y=10y+x-9

9x-9y=-9

x-y=-1,

So this is the system of equations to be solved:

x + y=11

x - y =-1

x=5, y=6

The number is 56.