Question 377809
Assume the original number is 10a+b where a,b are digits. Since the order of the digits is reversed upon adding 45, we have

10a + b + 45 = 10b + a

9a - 9b = -45

a - b = -5

We are also given a + b = 11. Adding the last two equations together we have 2a = 6 --> a = 3. From this we can plug into either of the last two equations to obtain b = 8. Therefore the original number is 38.