Question

The sum of the digits of a 2- digit number is 8. When we interchange the digits, it is found that the resulting new number is greater than the original by 18. What is the 2-digit number?​

Answer 1

$\large\underline{\sf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{digit \: at \: tens \: place \: be \: y} \\ &\sf{digits \: at \: ones \: place \: be \: x} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 10y + x} \\ &\sf{reverse \: number = 10x + y} \end{cases}\end{gathered}\end{gathered}$

According to statement,

The sum of the digits of a 2- digit number is 8.

$\red{\rm :\longmapsto\:x + y = 8 - - - (1)}$

According to second condition,

When we interchange the digits, it is found that the resulting new number is greater than the original by 18.

$\green{\rm :\longmapsto\:10x + y = 10y + x + 18}$

$\green{\rm :\longmapsto\:10x + y - 10y - x = 18}$

$\green{\rm :\longmapsto\:9x - 9y = 18}$

$\green{\rm :\longmapsto\:x - y = 2 - - - (2)}$

On adding equation (1) and (2), we get

$\rm :\longmapsto\:2x = 10$

$\bf :\longmapsto\:x = 5 - - - (3)$

On substituting the value of x in equation (1), we get

$\rm :\longmapsto\:5 + y = 8$

$\rm :\longmapsto\:y = 8 - 5$

$\bf :\longmapsto\:y = 3$

$\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{digit \: at \: tens \: place \: be \: 3} \\ &\sf{digits \: at \: ones \: place \: be \: 5} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 10y + x = 30 + 5 = 35} \\ &\sf{reverse \: number = 10x + y = 50 + 3 = 53} \end{cases}\end{gathered}\end{gathered}$

• Hence, Two digit number is 35.