Question

the difference between a 2-digit number and the number formed by reversing it's digits is 45. IF the sum of the digits of the original numbers is 13 then find the number
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Answer 1

Answer:

94

Step-by-step explanation:

let take original number =94

by reversing, it bcomes 49

94-49 =45

and 9+4 = 13

so, the right answer is 94

Answer 2

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

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

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

According to first condition

↝ Sum of the digits of two number is 13

$\rm \implies\:\boxed{ \tt{ \: x + y = 13 \: }} - - - - (1)$

According to second condition

The difference between a 2-digit number and the number formed by reversing it's digits is 45.

$\rm \implies\:(10x + y) - (10y + x) = 45$

$\rm \implies\:10x + y - 10y - x= 45$

$\rm \implies\:9x - 9y = 45$

$\rm \implies\:9(x - y )= 45$

$\rm \implies\:\boxed{ \tt{ \: x - y = 5 \: }} - - - - - (2)$

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

$\rm :\longmapsto\:x + y + x - y = 13 + 5$

$\rm :\longmapsto\:2x = 18$

$\bf\implies \:x = 9$

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

$\rm :\longmapsto\:9 + y = 13$

$\rm :\longmapsto\: y = 13 - 9$

$\bf\implies \:y = 4$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{digit \: at \: tens \: place \: be \: 9} \\ \\ &\sf{digits \: at \: ones \: place \: be \: 4} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{number \: formed = 10x + y = 10(9) + 4 = 94} \\ \\ &\sf{reverse \: number = 10y + x = 10(4) + 9 = 49} \end{cases}\end{gathered}\end{gathered}$

• Hence, Two digit number is 94.

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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.