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The correct answer is option 2: 411.
To understand why this is the correct answer, let`s analyze the problem.
We are given two-digit numbers, where the digits are reversed. Let`s assume the original number is 10a + b, where a and b are the digits. When the digits are reversed, the resulting number is 10b + a.
According to the problem, the number decreases by 27 when the digits are reversed. Therefore, we can express this as an equation:
10a + b - (10b + a) = 27
Simplifying the equation, we get:
9a - 9b = 27
Dividing both sides of the equation by 9, we get:
a - b = 3
So, a and b are two digits that have a difference of 3. We need to find the sum of all such two-digit numbers that meet this condition.
The two-digit numbers that satisfy this condition are 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98.
The sum of these numbers