Q39 of 44 Page 3

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. (CBSE 2006)

Let the two - digit number be xy (i.e. 10x + y).


After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).


According to question -


xy = 18


⇒ x = 18/y.....(1)


and,


(10x + y) - 63 = (10y + x)


⇒ 9x - 9y = 63


⇒ x - y = 7.....(2)


Substituting the value of x in equation (2), we get -



⇒ 18 - y2 = 7y


⇒ y2 + 7y - 18 = 0


⇒ y2 + 9y - 2y - 18 = 0


⇒ y(y + 9) - 2(y + 9) = 0


⇒ (y + 9)(y - 2) = 0


∴ y = 2


[y = - 9 is invalid because digits of a number cannot be negative.]


Substituting the value of y in equation (1), we get -


x = 9


Thus, the required number is 92.

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