The number we`re searching for can be represented as a simple equation: X = 124 + X/3. If we multiply all the terms by 3 to get rid of the fraction, we get: 3X = 372 + X. Simplifying it, we get 2X = 372 and thus X = 186.

Option 1: 194 is incorrect. If we plug in 194 into our equation, we would have 194 ≠ 124 + 194/3.

Option 2: 180 is also incorrect for the same reason. It wouldn`t satisfy the equation, 180 ≠ 124 + 180/3.

Option 3: Similarly, 189 does not fit the equation; 189 ≠ 124 + 189/3.

Option 4: 186 is the correct answer as it satisfies the equation, 186 = 124 + 186/3. Therefore, the number that is 124 more than its one-third is indeed 186.