To find the missing number in the series 242, 393, 4164, we need to identify the pattern or rule followed in the series.

The difference between the first two numbers is 393 - 242 = 151.
The difference between the second and third numbers is 4164 - 393 = 3771.

Looking at these differences, we can observe that they are increasing by a factor of 25 each time. Let's see if this pattern holds for the next number.

The difference between the third and fourth numbers would be 3771 + 25 = 3796.

Now, we can find the missing number by adding the difference to the last number in the series.

4164 + 3796 = 7960.

However, none of the given options match this result. So, let's analyze the given options to find an alternative pattern that might be followed in the series.

Option A: 5525
If we subtract the first number (242) from the second number (393), we get 393 - 242 = 151. The difference between the second and third numbers (393 and 5525) is 5525 - 393 = 5132. This pattern does not align with the previous differences observed in the series, so option A is not the correct answer.

Option B: 5255
Similarly, if we subtract the first number (242) from the second number (393), we get 393 - 242 = 151. The difference between the second and third numbers (393 and 5255) is 5255 - 393 = 4862. This pattern aligns with the previous differences observed in the series, so option B is a possible answer.

Option C: 5235
The difference between the second and third numbers (393 and 5235) is 5235 - 393 = 4842. This pattern does not align with the previous differences observed in the series, so option C is not the correct answer.

Option D: 5325
The difference between the second and third numbers (393 and 5325) is 5325 - 393 = 4932. This pattern does not align with the previous differences observed in the series, so option D is not the correct answer.

Therefore, the missing number in the series is 5255 (option B).