Two pipes P and Q fill a container in 12 min. and 15 min. respectively, while a drain valve ‘R’ empties the full container in 6 min. Keeping P and Q active for the initial 5 min., valve ‘R’ is subsequently opened. In what duration is the container completely emptied?
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Answer: D. 45 min
Explanation
Calculating the water filled by pipes P and Q in five minutes gives three quarters of the tank. Opening the drain valve creates a negative net flow rate combining all three active valves. Dividing the remaining water volume by the negative net rate determines forty five minutes to empty. Multi stage word problems require calculating partial work completions before introducing new variables. Drain valves contribute negative work rates in cistern filling and emptying equations. Time calculations for emptying tanks divide remaining volume by the net negative discharge rate.
Industrial batch processing plants manage sequential valve operations to control chemical tank levels. Emergency drainage systems are evaluated using multi pipe discharge rate calculations. Fluid mechanics applications require precise timing when sequencing filling and emptying operations. Option A suggests thirty minutes which underestimates the time needed to empty the container. Option B proposes thirty five minutes which fails to match the net rate calculation. Option C offers forty minutes which results from a minor arithmetic error in the final step.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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