Two taps can fill a cistern in 4 hours and 27 hours respectively.
Two taps can fill a cistern in 4 hours and 27 hours respectively. A third tap can empty it in 27 hours. How long (in hours) will it take to fill one-fourth of the empty cistern, if all of them are opened together?
दो नल एक टंकी को क्रमशः 4 घंटे और 27 घंटे में भर सकते हैं। तीसरा नल उसी टंकी को 27 घंटे में खाली कर सकता है। यदि सभी नल एक साथ खोल दिए जाएँ, तो खाली टंकी का एक-चौथाई भाग भरने में कितना समय (घंटों में) लगेगा?
Detailed Solution & Logic
Correct Answer:
1
Let total work (tank capacity) = 1 unit.
Rates:
- First tap fills in 4 hours → $1/4$ per hour
- Second tap fills in 27 hours → $1/27$ per hour
- Third tap empties in 27 hours → $-1/27$ per hour
Now combine all three:
Net rate = $1/4 + 1/27 - 1/27 = 1/4$
So effectively, only the first tap works.
Now we need to fill one-fourth of the tank = $1/4$
Time = work ÷ rate = $(1/4) ÷ (1/4) = 1$ hour
Final Answer: 1 hour (Option: 1)
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