OFFICIAL EXPLANATION:
The original sentence begins with a modifier ("Before its independence") that clearly describes India, though the subject of the main clause is Britain. Moreover, "ruled India as a colony" is wordy and the verb "ruled" is in the simple past when it would be better in the past perfect (two past actions, one of which was earlier). Finally, "they" has no grammatical antecedent and "would" is not a proper tense here (the simple past is required).
(A) This choice is incorrect as it repeats the original sentence.
(B) Britain should not be the recipient of the modifier "Before its independence."
(C) The pronoun "they" has no logical antecedent. Logically it probably refers to the British, but the British do not appear in the sentence. Also, the past perfect tense would have been preferable here (had been ruled) since the ruling occurred before the relinquishing of the power.
(D) The phrase "ruled as a colony by Britain" is awkward and unclear. The placement of the modifier "by Britain" makes it unclear that the ruling is being done by Britain.
(E) CORRECT. This correctly places India as the recipient of the opening modifier. The past perfect is utilized to indicate that different times in the past. Notice that the word "ruled" has been removed from this answer choice, however, this did not result in a change of meaning. To be a colony of the British is to be ruled by the British. The exclusion of the pronoun its in the beginning of the sentence (see answer choices A and C) is incidental. The sentence would have been correct with the pronoun its as well.