Answer:
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
[tex]\implies 20x + 2y - 1 = 10y + x[/tex]
[tex]20x + 2y - 10y - x = 1[/tex]
[tex]19x - 8y = 1[/tex] ...... (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 )
