The difference between a two-digit number and the number obtained by reversing its digits is 45. Which of these could be the original number?

For a number $10a+b$, the difference $(10a+b)-(10b+a)=9(a-b)$. So $9(a-b)=45$ means the digits differ by 5. Only 72 has digits differing by 5 $(7-2=5)$, and indeed 72 − 27 = 45. The others give differences of 3, 3 and 8 respectively.