Discussion
A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number ?
Answer: A
The number is 47.
Let the number be \(10a + b\) with \(a + b = 11\). Adding 27 reverses the digits:
\[ \begin{aligned} 10a + b + 27 &= 10b + a \\ 9(b - a) &= 27, \quad b - a = 3 \end{aligned} \]
With \(a + b = 11\), \(a = 4\) and \(b = 7\): the number is 47, and \(47 + 27 = 74\). 65, 83 and 92 also have digit sums of 11, but adding 27 does not reverse them.
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