Discussion

The sum of the digits of a 2-digit number is 9. When 27 is added to the number, the digits get reversed. The number is:

Answer: B

Let the ten's digit be x and the unit's digit be y. Number = 10x + y.

Given: x + y = 9.

Given: (10x + y) + 27 = 10y + x (reversed number).

\(9x - 9y = -27\), which simplifies to \(x - y = -3\) or \(y - x = 3\).

We have two equations: x + y = 9 and y - x = 3.

Adding them: 2y = 12, so y = 6.

Substituting y=6 into x+y=9, we get x=3.

The number is 36.

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