Two valves X and Y fill a basin in 15 hrs. and 20 hrs. respectively, while a third pipe ‘Z’ empties the full basin in 25 hrs. All three activate initially, but valve ‘Z’ is closed after 10 hrs. How much time is needed to completely fill the basin?
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Answer: A. 12 hrs
Explanation
Pipes X and Y fill portions of the basin while pipe Z empties it concurrently. Calculating the net work done during the first ten hours accounts for all three active valves. Determining the remaining volume after valve Z closes allows calculation of the final twelve hours duration. Basin filling problems combine inflow rates from multiple taps while subtracting outflow rates from drainage pipes. Sequential valve operations require breaking the total timeline into distinct operational phases. Net rate equations dictate that filling speed equals total inlet rates minus outlet drainage rates.
Reservoir management requires calculating fluid levels when emergency drainage valves are opened and closed. Industrial chemical tanks use multiple filling and emptying valves that must be managed sequentially. Plumbing engineers design multi-inlet water storage systems to handle complex operational adjustments. Option B overestimates the total time by miscalculating the net flow rate after valve Z closes. Option C assumes a slower filling rate during the final operational phase of the basin. Option D is incorrect because the remaining volume fills faster than eighteen hours suggest.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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