Two taps can fill a cistern in 4 hours and 38 hours respectively.
Two taps can fill a cistern in 4 hours and 38 hours respectively. A third tap can empty it in 38 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 38 घंटे में भर सकते हैं। तीसरा नल उसे 38 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
1
Step 1: Rates
Filling taps:
- First tap = $1/4$ tank per hour
- Second tap = $1/38$ tank per hour
Emptying tap:
- Third tap = $-1/38$ tank per hour
Step 2: Net rate
Net rate = $1/4 + 1/38 - 1/38$
$1/38$ cancels out
So net rate = $1/4$ tank per hour
Step 3: Time for 1/4 tank
If rate = $1/4$ tank per hour, then time for $1/4$ tank:
Time = 1 hour
Final Answer: 1 hour
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