Discussion
The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.
Answer: A
The original number is 39.
Let the tens digit be \(a\) and the units digit \(b\). The number is \(10a + b\) and its reverse is \(10b + a\).
\[ \begin{aligned} a + b &= 12 \\ (10b + a) - (10a + b) &= 9(b - a) = 54 \\ b - a &= 6 \\ a = 3,\ b &= 9 \end{aligned} \]
Check: 93 - 39 = 54. 93 has the right digits but reversing it gives a smaller number. 57 reversed is 75, larger by only 18, and 66 reversed is unchanged.
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