sum of digits of two digit number is 9. If we interchange the digit than sum of original number and new number is 99. Find the ori

1 thought on “sum of digits of two digit number is 9. If we interchange the digit than sum of original number and new number is 99. Find the ori”

1. [tex]\large\underline{\sf{Solution-}}[/tex]

   [tex]\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{digit \: at \: ones \: place \: = x} \\ &\sf{digit \: at \: tens \: place \: = y} \end{cases}\end{gathered}\end{gathered}[/tex]

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

   According to first condition,

   Sum of the digits of 2 digit number is 9

   [tex]\bf :\longmapsto\:x + y = 9 – – (1)[/tex]

   According to second condition,

   Sum of original number and number formed by interchanging the digits is 99.

   [tex]\rm :\longmapsto\:10y + x + 10 + y = 99[/tex]

   [tex]\rm :\longmapsto\:11x + 11y = 99[/tex]

   [tex]\rm :\longmapsto\:x + y = 9[/tex]

   So, possible pairs so that x + y = 9

   [tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 9 \\ \\ \sf 1 & \sf 8 \\ \\\sf 2 & \sf 7 \\ \\ \sf 3 & \sf 6 \\ \\\sf 4 & \sf 5 \\ \\ \sf 5 & \sf 4 \\ \\ \sf 6 & \sf 3 \\ \\\sf 7 & \sf 2 \\ \\\sf 8 & \sf 1 \\ \\ \sf & \sf \end{array}} \\ \end{gathered}[/tex]

   So, possible 2 digit numbers are 90, 81, 72, 63, 54, 45, 36, 27, 18

   Basic Concept Used :-

   Writing Systems of Linear Equation from Word Problem.

   1. Understand the problem.

   • Understand all the words used in stating the problem.

   • Understand what you are asked to find.

   2. Translate the problem to an equation.

   • Assign a variable (or variables) to represent the unknown.

   • Clearly state what the variable represents.

   3. Carry out the plan and solve the problem.

   Reply