Let's assume that the number of candidates who applied initially is 'x'.

Given that the ratio of selected to unselected candidates is 2:1, we can assume that there are 2k selected candidates and k unselected candidates.

So, initially, the total number of candidates who applied is x, and the number of selected candidates is 2k. The number of unselected candidates can be calculated as x - 2k.

According to the given condition, if 50 less had applied and 25 less had been selected, the ratio of selected to unselected candidates would have been 9:4.

So, the number of candidates who would have applied in this scenario would be x - 50, and the number of selected candidates would be 2k - 25. The number of unselected candidates in this scenario can be calculated as (x - 50) - (2k - 25).

Given that the ratio of selected to unselected candidates in this scenario is 9:4, we can write the equation as:

(2k - 25) / ((x - 50) - (2k - 25)) = 9/4

Simplifying the equation, we get:

8k - 100 = 9x - 450 - 9k + 225
17k - 325 = 9x - 450

Rearranging the equation, we get:

9x - 17k = 125

Since we need to find the value of x, we need one more equation.

We can use the fact that the number of unselected candidates in the initial scenario is x - 2k. According to the given ratio, the number of unselected candidates is 4k.

So, we can write the equation as:

x - 2k = 4k

Simplifying the equation, we get:

x = 6k

Now, we have two equations:

9x - 17k = 125
x = 6k

Substituting x = 6k in the first equation, we get:

9(6k) - 17k = 125
54k - 17k = 125
37k = 125
k = 125/37

Substituting the value of k in x = 6k, we get:

x = 6(125/37)
x = 750/37

Approximating the value, we get:

x ≈ 20.27

Since the number of candidates cannot be a fraction, we can conclude that the number of candidates who had applied is approximately 20.27. However, this contradicts the given options, so there might be an error in the question or the options provided.