The best answer is option E.
Option A: The main reason for the
decline in worldwide illiteracy rates,
which have dropped over the last 20 years, is the sharp increase of literacy rates among young women, which is the result of campaigns to increase educational opportunities for girls. This is wordy compared with option E. The use of decline and which have dropped creates redundancy, which was avoided by option E.
Option B:
Declining over the last 20 years, worldwide illiteracy rates
have fallen for one main reason, which is the sharp increase of literacy rates among young women, which is the result of campaigns to increase educational opportunities for girls. Option B also has a redundancy issue creating a wordy option compared with option E.
Option C:
Declining over the last 20 years, the main reason for the fall in illiteracy rates is the sharp increase of literacy rates among young women, which is the result of campaigns to increase educational opportunities for girls.
Declining over the last 20 years is a dangling modifier intended to modify illiteracy rates, instead, it erroneously modifies the main reason.
Option D: The main reason worldwide illiteracy rates,
having dropped over the last 20 years is the sharp increase of literacy rates among young women,
which is the result of campaigns to increase educational opportunities for girls. This is grammatically not correct. The sentence is incomplete and makes no sense whatsoever.
Option E: The main reason for the decline in worldwide illiteracy rates over the last 20 years is the sharp increase of literacy rates among young women, which is the result of campaigns to increase educational opportunities for girls. This is the best answer out of the lot. Compared with options A and B, it is more concise.