The sum of the digits of a two-digit number is 9. If 27 is addedto it, the digits of the number get reversed. The number is

Sure, let's solve the problem step by step:

Let's assume the two-digit number is represented as "10x + y", where x represents the tens digit and y represents the units digit.

According to the problem, the sum of the digits is 9. So, we can write the equation as:

x + y = 9 ----(1)

It is also given that when 27 is added to the number, the digits get reversed. So, we can write the equation as:

10y + x + 27 = 10x + y ----(2)

Now, let's solve the equations (1) and (2) to find the values of x and y.

From equation (1), we can express x in terms of y as:

x = 9 - y

Substituting this value of x in equation (2), we get:

10y + (9 - y) + 27 = 10(9 - y) + y

Simplifying the equation, we get:

10y + 9 - y + 27 = 90 - 10y + y

Combining like terms, we get:

9y + 36 = 90 - 9y

Bringing all the y terms to one side, we get:

9y + 9y = 90 - 36

18y = 54

Dividing both sides by 18, we get:

y = 3

Substituting this value of y in equation (1), we get:

x + 3 = 9

Subtracting 3 from both sides, we get:

x = 6

Therefore, the two-digit number is 63.