After adding two consecutive two-digit numbers and reversing the result, we will get the bigger one of the two addends.

Find the two consecutive two-digit numbers.

The two consecutive two-digit numbers would be 36 and 37.

Step-by-step explanation:

Consider a 2 digit number 10x + y ( where x and y must be integers from 0 to 9 )

Then the previous 2 digit number number = 10x + y -1

That is, 10x + y - 1 and 10x + y are two digits consecutive numbers ( where y ≠ 0, if x = 1 ).

10x +y - 1 + 10x + y = 20x + 2y - 1

Now, according to the question,

After reversing digits of 20x + 2y - 1 ,  10x + y is obtained.

That is, if we reverse digits of 10x + y, 20x + 2y - 1 will obtain.

But, after reversing digits of 10x + y, new number = 10y + x

            ...... (1)

Here, x∈{0,1,2,3,4,5,6,7,8,9} , y∈{0,1,2,3,4,5,6,7,8,9}.

Only if x = 3 and y = 7

Equation (1) holds.

10x + y = 10(3) + 7 = 30 + 7 = 37

10x + y - 1 = 36

Therefore, the consecutive numbers are 36 and 37.

Verification:

37 + 36 = 73 ( which is obtained after reversing the digits of 37 )