The sum of a two-digit number and the number obtained by reversing the digits is 99. If the digits of the number differ by 5, then the two-digit number can be:

Correct option is A

Given :

The sum of a two-digit number and the number obtained by reversing the digits is 99.

The digits of the number differ by 5

Solution: 

Let the digit be x and y 

Then, the number be 10x + y 

The sum of a two-digit number and the number obtained by reversing the digits is 99.

$$(10x + y) + (10y + x ) = 99$$ 

$$10x + y + 10y + x = 99$$ 

$$11x + 11y = 99$$  (divide by 11)

$$x + y = 9......(1)$$

The digits of the number differ by 5

$$x - y = 5$$ ....(2)

adding equation (1) and (2):

$$x + y + x- y = 14$$ 

$$2x = 14$$ 

$$x = 7$$  

Then, the value of y

$$7 - y = 5$$ 

$$y = 2$$ 

Thus, the two digit number is 27