Question

The units digit of a two-digit number is twice the tens digit. When the digits are reversed, the new number is 36 more than the original number. Find the original and new numbers
Pls help me with full solution

Answer 1

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answer in attachment

Answer 2

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

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

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

According to first condition,

The unit digit of a two digit number is twice the tens digit.

$\rm :\longmapsto\:x = 2y - - - (1)$

According to second condition,

When digits are reversed, the new number is 36 more than the original number.

$\rm :\longmapsto\:10x + y = 10y + x + 36$

$\rm :\longmapsto\:9x - 9y = 36$

$\rm :\longmapsto\:x - y = 4$

$\rm :\longmapsto\:2y - y = 4 \: \: \: \: \: \{using \: (1) \}$

$\bf\implies \:y = 4$

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

$\bf\implies \:x = 8$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 10y + x = 48} \\ &\sf{reverse \: number = 10x + y = 84} \end{cases}\end{gathered}\end{gathered}$

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.