# 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.

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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