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.