The sum of the digits of a 2-digit number is 17. If we add 9 to the number, the new number obtained is a number formed by interchange of the digits. Find the number.

Let the ten's digit be x and the unit's digit be y.
The number can be written value-wise as 10x+y.

Given that the sum of the digits is 17:

x+y=17— (Equation 1)
When 9 is added to the number, the digits are interchanged (new number becomes 10y+x):

(10x+y)+9=10y+x
10x−x+y−10y=−9
9x−9y=−9
Dividing by 9:

x−y=−1— (Equation 2)
Now, adding Equation 1 and Equation 2:

(x+y)+(x−y)=17+(−1)
2x=16⟹x=8
Substitute x=8 back into Equation 1:

8+y=17⟹y=9
So, the original number is 10x+y=10(8)+9=89.