If you take a particular two digit number reverse its digits to make a second two digit number and add these two numbers together, their sum will be 121. What is the original number

First number is 10a+b

second number is 10b+a

sum is 10a+10b+a+b=121

11a+11b=121

11 (a+b) = 121

(a+b) = 11

the two digits sum to 11. there are now free enough choices to try them all. the smaller of the 2 numbers must be 29, 38, 47, or 56. of the 4 only 56 (or 65) can be the original number