Question

A number consists of two digits whose sum is 10. If 18 is added to the number, the digits are interchanged. The number is

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,

Sum of the digits of a two digit number is 10

$\bf :\longmapsto\:x + y = 10 - - - - (1)$

According to statement again,

If 18 is added to the original number, the digits interchange their place.

$\rm :\longmapsto\:10y + x + 18 = 10x + y$

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

$\rm :\longmapsto\:9x - 9y = 18$

$\bf :\longmapsto\:x - y = 2 - - - (2)$

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

$\bf :\longmapsto\:2x = 12$

$\bf\implies \:x = 6 - - (3)$

On substituting x = 6 in equation (1), we get

$\rm :\longmapsto\:6 + y = 10$

$\bf\implies \:y = 4 - - (4)$

$\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{digit \: at \: tens \: place \: be \: 4} \\ &\sf{digits \: at \: ones \: place \: be \: 6} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: The \: number \: is - \begin{cases} &\sf{10 \times 4 + 6 \times 1 = 46}\end{cases}\end{gathered}\end{gathered}$

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.