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 ?

Answer: Option A

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.