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Question 75
Pipe A could fill an empty cistern in 18 hours while Pipe B can drain filled cistern in 30 hours. When the cistern is empty. Pipe A is turned on for an hour and then turned off. Now Pipe B is allowed to drain out water from the cistern for an hour and then turned off. The pipes were alternately left open for an hour each time till the cistern was full. How much time did it take for the cistern to be full?
Solution
A can fill the cistern in 18 hours and B can empty in 30 hours
LCM of 18 and 30 is 90 units
In one hour A can fill 5 units
In one hour B can empty 3 units
So in 2 hours 2 units of work is done
For 86 hours 86 units of work is done
Now that 4 units is filled by A in 4/5 hours
So total time 86 hours 48 minutes
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