Question

solve this question

Answer 1

let the number be xy
product of digits are 12,so xy= 12
number is represented as 10x+y
$10x + y + 36 = 10y + x \\ 10x - x + y - 10y = - 36 \\ 9x - 9y = - 36 \\ x - y = - 4 \\ place \: - y = - 4 - x \\ y = 4 + x \: \: \: \: \: in \: the \: first \: equation \\ x(4 + x) = 12 \\ {x}^{2} + 4x - 12 = 0 \\ {x}^{2} + 6x - 2x - 12 = 0 \\ x(x + 6) - 2(x + 6) = 0 \\ (x + 6)(x - 2) = 0 \\ x = - 6 \\ x = 2$
put these values in eq to find the values of y
$y = \frac{12}{x} \\ y = \frac{12}{2} = 6 \\ y = \frac{12}{ - 6} = - 2$
now take both positive values .The number can be 26.
or the number can be -62( putting x=-6,y=-2)