"Estimating" (answer C) is the correct answer because you need an action that "works well when applying..." If you replace all these words with the auxiliary verb "to do," it becomes clearer: "Although doing this works well when doing that..." It is possible to make a sentence with "Although estimated expenses work well when...," but then the next word would need to be a noun (e.g., "Although estimated expenses work well when data is incomplete,..."). Also, notice how "works" is plural in the example sentence: this is because it is paired with a verb (estimating). If you choose "estimated expenses," then "estimated" would be an adjective modifying "expenses"—since "expenses" is plural here, the next verb would need to be "work," in the singular form. So the person writing the quiz actually gave you a big hint here to the correct answer!

It is estimating. If you said " I estimated expenses when I applied for..." to stay in thge same tense throughout the sentence.