A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number?

Let the ten's digit be x. Then, unit's digit = (11 - x).

So, number = 10x + (11 - x) = 9x + 11.

Therefore (9x + 11) + 27 = 10 (11 - x) + x ⟺ 9x + 38 = 110 - 9x ⟺ 18x = 72 ⟺ x = 4.

Thus, ten's digit = 4 and unit's digit = 7.

Hence, required number = 47.