A number consists of two digits whose sum is 10. If 18 is subtracted form the number, its digits are reversed. Find the number.

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A number consists of two digits whose sum is 10. If 18 is subtracted form the number, its digits are reversed. Find the number.

Solution:

Suppose the ones digit and tens digit be $x$ and $y$ respectively.
Then according the question
$\begin{array}{l} \mathrm{x}+\mathrm{y}=10\dots \dots(i) \\ (10 \mathrm{y}+\mathrm{x})-18=10 \mathrm{x}+\mathrm{y} \\ \mathrm{x}-\mathrm{y}=-2\dots \dots(ii) \end{array}$
Adding equation(i) and equation(ii), we obtain
$2 x=8 \Rightarrow x=4$
Now, putting $x=4$ in equation(i), we get
$4+y=10 \Rightarrow y=6$
As a result, the number is 64 .