Question

A two digit number is such that the product of its digit is $18$. When $63$ is subtracted from the numbers the digit interchange their place, Find the number .
A) $92$
B) $56$
C) $88$
D) $71$

Answer 1

Hint:First let us take the tens place of the digit is $y$ and ones place of the digit is $x$ hence the number became $10y + x$ so from the given question condition that $63$ is subtracted from the number the digit interchange their place then equation will be $10y + x$ $ - 63$ = $10x + y$ and it is given product of two numbers is $18$ i.e $xy = 18$ from these two equations find the value of $x$ and $y$ .

Complete step-by-step answer:
Let us take the tens place of the digit is $y$ and ones place of the digit is $x$ hence the number became $10y + x$
For example
If let us suppose that number is $89$ then its tens place is $8$ and ones place is $9$ hence it can be written as $10 \times 8 + 9$ .
Now it is given that the product of its digit is $18$ .
mean that $xy = 18$
Now in the question it is given that the if we subtracted $63$ from this number then the digit will interchange ,
Interchange means if initial the tens place of the digit is $y$ and ones place of the digit is $x$ then if interchanging is happen then the tens place of the digit is $x$ and ones place of the digit is $y$
So from the given question ,
$10y + x$ $ - 63$ = $10x + y$
$9y - 9x$ $ - 63$= $0$
Divide by $9$ in whole equation ,
$y - x - 7 = 0$
$x = y + 7………….(1)$
In question they given the product of two numbers is $18$ then we can write,
$xy = 18……………(2)$ ,
Substitute equation (1) in (2) we get,
$(y + 7)y = 18$
${y^2} + 7y - 18 = 0$
On solving this
${y^2} + 9y - 2y - 18 = 0$
$y(y + 9) - 2(y + 9) = 0$
$(y - 2)(y + 9) = 0$
Hence $y = - 9,2$
We know that $x = y + 7$ therefore $x = - 2,9$
So the number is $92$ or $ - 29$
Neglect the $- 29$ number as it does not satisfy the equation (2)
So the number is $92$
So, the correct answer is “Option A”.

Note:Try to verify the solution by substituting the value which we got in equation (1) and (2).Subtracting number $63$ from the number $92$ we get $29$ in which digit interchanged their place and also product of their digits gives $18$, Hence, It satisfies all the conditions and our answer is correct.A linear equation $ax + by + c = 0$ is represented graphically as a straight line. Every point on the line is a solution for the linear equation. Every solution of the linear equation is a point on the line.Certain linear equations exist such that their solution is $(0,0)$ . Such equations when represented graphically pass through the origin.