Question

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

Answer 1

Let the ones digit and tens digit be x and y respectively.
Then as per the question
$$\begin{gathered} x+y=10.....\left(i\right) \\ \left(10y+x\right)-18=10x+y \\ x-y=-2.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$2x=8\Rightarrow x=4$
Now, putting x = 4 in (i), we have
$4+y=10\Rightarrow y=6$
Hence, the number is 64.