Question

• 3.The sum of the digits of a two digit number is 12. The number
obtained by interchanging the digits exceeds the given number by 18.
Find the number?
​

Answer 1

Answer:

Required Number = (10x+y). Number obtained on reversing the digits = (10y+x). Hence, the required number is 57.25

Step-by-step explanation:

please follow

Answer 2

Basic Concept Used :-

Writing System of Linear Equations 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.

Let's solve the problem now!!

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

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

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

According to statement,

Sum of the digits of two digit number is 12.

$\bf\implies \:x + y = 12 - - - (1)$

According to statement again

The number obtained by interchanging the digits exceeds the given number by 18.

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

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

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

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

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

$\rm :\longmapsto\:2x = 14$

$\bf\implies \:x = 7$

On substituting x = 7, on equation (1), we get

$\rm :\longmapsto\:7 + y = 12$

$\bf\implies \:y =5$

$\begin{gathered}\begin{gathered}\bf\: It \: means-\begin{cases} &\sf{digit \: at \: ones \: place \: be \: x = 7} \\ &\sf{digit \: at \: tens \: place \: be \: y = 5} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:Hence - \begin{cases} &\sf{number \: formed = 10 \times 5 + 7 = 57}\end{cases}\end{gathered}\end{gathered}$