Explanation:

Let two digit number= 10y + x

According to question,

1^st condition, 10y  + x = k(x + y) ….(1)

2nd condition, 10x + y = m(x + y)….(2)

Adding (1) and (2) we get

11x + 11y = (k + m) = (x + y)

11(x + y) = (k + m)(x + y)

k + m = 11 => m = 11 − k