The sum of the digits of a two-digit number is 9. If 27 is addedto it, the digits of the number get reversed. The number is(A) 25 (B) 72 (C) 63 (D) 36

To solve this problem, let's assume the two-digit number is represented by the digits "a" and "b".

According to the given information, the sum of the digits is 9. So, we can write the equation: a + b = 9.

Next, we are told that if 27 is added to the number, the digits get reversed. This means that the new number will be represented by the digits "b" and "a". So, we can write the equation: 10b + a + 27 = 10a + b.

Now, we can solve these two equations simultaneously to find the values of "a" and "b".

From the first equation, we can express "a" in terms of "b" as: a = 9 - b.

Substituting this value of "a" in the second equation, we get: 10b + (9 - b) + 27 = 10(9 - b) + b.

Simplifying this equation, we have: 10b + 9 - b + 27 = 90 - 10b + b.

Combining like terms, we get: 9b + 36 = 90 - 9b.

Moving all the terms to one side, we have: 18b = 54.

Dividing both sides by 18, we find: b = 3.

Substituting this value of "b" in the first equation, we get: a + 3 = 9.

Solving for "a", we find: a = 6.

Therefore, the two-digit number is 63.

Hence, the correct answer is (C) 63.