Question

The sum of the digits of a two digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27. Find the number

IT IS FROM LINEAR EQUATION IN ONE VARIABLE.
YOU CAN USE ONLY ONE VARIABLE​

Answer 1

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

Given that,

The sum of the digits of a two digit number is 7.

So,

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\: Let-\begin{cases} &\sf{digit \: at \: tens \: place \: be \: x} \\ &\sf{digits \: at \: ones \: place \: be \: 7 - x} \end{cases}\end{gathered}\end{gathered}$

Thus,

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 10(x)+ 7 - x = 9x + 7} \\ &\sf{reverse \: number = 10(7 - x)+ x =70 - 9x} \end{cases}\end{gathered}\end{gathered}$

According to statement

The number obtained by interchanging the digits exceeds the original number by 27.

$\rm :\longmapsto\:70 - 9x - (9x + 7) = 27$

$\rm :\longmapsto\:70 - 9x - 9x - 7= 27$

$\rm :\longmapsto\:63 - 18x = 27$

$\rm :\longmapsto\:- 18x = 27 - 63$

$\rm :\longmapsto\:- 18x = - 36$

$\bf\implies \:x = 2$

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\: So-\begin{cases} &\sf{digit \: at \: tens \: place \: be \: 2} \\ &\sf{digits \: at \: ones \: place \: be \: 7 - 2 = 5} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 9x + 7 = 18 + 7 = 25} \\ &\sf{reverse \: number =70 - 9x = 70 - 18 = 52} \end{cases}\end{gathered}\end{gathered}$

$\red{\bf\implies \:\boxed{ \tt{ \: Number \: is \: 25 \: \: }}}$