Question

the addition of 2 digit number is 9 when we add 45 to number digits are inverse

Answer 1

Solution:-
Let us assume that 'x' is at ten's place and 'y' is at unit's place in the original number. So the value of the original number is 10x + y.
If we add 45 to the original number then the digits are reversed. So, the new number will be 10y +x.
So, according to the question.
(10y + x) = (10x + y) + 45
10y - y = 10x - x + 45
(9y = 9x + 45) 
dividing it by 5, we get
y = x + 5  
As sum of the two digits of this number is 9.
So, 
x + y = 9 ..............(1)
Substituting the value of y = x + 5 in the equation (1), we get
x + x + 5 = 9
2x = 9 - 5
2x = 4
x = 2
So, y = 9 - 2
y = 7
So, the required number is 27. If we add 45 to it the digits are reversed and the number becomes 72.