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# 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. Find the number.

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In this Question A two-digit number is such that the product of its digit is given. if a number is substracted to the number, the digits interchange their places.
You have to find the number.
This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.
This is the Question Number 17 Of Exercise 3E of RS Aggarwal Solution.

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1. Solution :-
Let the tens place digit be x.
And the units place digit be y.
According to the Question,
⇒ xy = 18
⇒ y = 18/x …..(i)
And, (10x + y) – 63 = 10y + x
⇒ 9x – 9y = 63
⇒ x – y = 7 …. (ii)
Putting y’s value in Eq (ii), we get
⇒ x – 18/x = 7
⇒ x² – 18 = 7x
⇒ x² – 7x – 18 = 0
⇒ x² – 9x + 2x – 18 = 0
⇒x(x – 9) + 2(x – 9) = 0
⇒ (x – 9) (x + 2) = 0
⇒ x – 9 = 0 or x + 2 = 0
⇒ x = 9, – 2 (As x can’t be negative)
⇒ x = 9
Putting x’s value in Eq (i), we get
⇒ xy = 18
⇒ 9y = 18
⇒ y = 18/9
⇒ y = 2
Number = 92
Hence, the required number is 92

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