There are total 12 pipes to fill a reservoir in which some are fill pipes where as some are empty pipes. A fill pipe takes 30 minutes to fill reservoir completely, which is 60 minutes less than the time taken by an empty pipe to empty the reservoir. All working together takes 4.5 hr to completely fill the reservoir. If now one empty pipe starts working as fill pipe, what will be the time taken to fill the reservoir completely?

Fill pipe rate = 1/30 reservoir per minute. Empty pipe rate = 1/90 reservoir per minute. Let f = fill pipes, (12-f) = drain pipes. Combined rate = f/30 - (12-f)/90 reservoirs per minute = (3f - 12 + f)/90 = (4f - 12)/90. Time = 4.5 hours = 270 minutes. So 270 × (4f - 12)/90 = 1 → 3(4f - 12) = 1 → 12f - 36 = 1 → 12f = 37 → f = 37/12 ≈ 3.08. This isn't an integer - there's an inconsistency. If one drain becomes fill, new configuration still doesn't match given options. The calculated time (with corrected values) differs from all options A-D, so E is correct.