First number is
Reverse the digits, you get
add the two to get
so you must have . Possible choices (up to reversing the digits) are .
I'm assuming that when you say you "take two-digit number to make a second two-digit number", you make the second number by reversing the digits.
Let x be the first digit, and y be the second digit.
Your first number is x + 10y, so your second number is 10x + y
When you add the two numbers together you have
(x + 10y) + (10x + y) = 10x + x + 10y + y = 11x + 11y = 11(x + y) = 121
So x + y = 11
Remember, x and y represent the digits, so they are single digit numbers.
So, we have:
x y
2 9
3 8
4 7
5 6
6 5
7 4
8 3
9 2
i.e. 29 + 92 = 38 + 83 = 47 + 74 = 56 + 65 = 65 + 56 = 74 + 47 = 83 + 38 = 92 + 29 = 121