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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?

Correct Answer: 47

Explanation:

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.

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