Question

The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.

Answer 1

Let the number at the ten's place be x and that at the one's place be y.
Number obtained = 10x + y
The sum of the digits in a two-digits number is 9.
$x+y=9$ .....(I)
The number obtained by interchanging the digits exceeds the original number by 27.
$$\begin{gathered} 10y+x-\left(10x+y\right)=27 \\ \Rightarrow 10y+x-10x-y=27 \\ \Rightarrow 9y-9x=27 \\ \Rightarrow y-x=3.....\left(\mathrm{II}\right) \end{gathered}$$
Adding (I) and (II)
$$\begin{gathered} 2y=12 \\ \Rightarrow y=6 \end{gathered}$$
x = 3
Thus, the number is 36.