This question is taken from linear equations in two variables in which we have to find the number a two digit number is such that the product of its digits is 18. When 63 is subtracted from the number. the digits interchange their places.

Kindly give me a detailed solution of this question

Book – RS Aggarwal, Class 10, chapter 3E, question no 17

## Let the tenth digit be x. Then, the units digits=18/x

Number =10x+18/x

and Number obtained by interchanging the digits=10x×18/x+x

∴(10x+18/x)−(10×18/x+x)=63

⇒10x+18/x−180/x−x=63

⇒9x−162/x−63=0

⇒9x²−63x−162=0

⇒x²−7x−18=0

⇒x=9

or x=−2

But, a digit can never be negative, So, x=9

hene, the required number =(10×9)+18/9=92