The sum of the digits of a two-digit number is (9). The difference between the number and the number with reversed digits is (27). What is the original number?

Correct answer: 63

Let the tens digit be \(x\) and the units digit be \(y\). Then \(x+y=9\). Taking the question to mean that the original number is 27 greater than its reversed number, \((10x+y)-(10y+x)=27\). Thus \(9(x-y)=27\), so \(x-y=3\). Solving the two equations gives \(x=6\) and \(y=3\). Therefore, the original number is \(63\). Although 54 has digit sum 9, its difference from 45 is only 9. Exam tip: represent a two-digit number as \(10x+y\) and its reverse as \(10y+x\).