Question

a two digit number is such that the product of the digits is 8. when 18 ia added to theer is reversed. the number is number then the numb

Answer 1

Let the digit at tens place be x and at unit place be y. Given
$xy = 8 - - - (1) \\ (10 + y) + 18 = 10y + x \\ 9x - 9y + 18 = 0 \\ x - y + 2 = 0 \\ substituting \: \: y \: \: from \: \: (1) \\ x - \frac{8}{x} + 2 = 0 \\ {x}^{2} + 2x - 8 = 0 \\ (x + 4)(x - 2) = 0 \\ x = - 4 \: \: or \: \: 2 \\ therefore \: \: y = - 2 \: \: or \: \: 4$
Thus the numbers are -42 or 24