A cistern can be filled by a tap in 6 hours and emptied by an outlet pipe in 8 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together ?
Time taken to fill cistern by a tap = 6hrs
Cistern filled by a tap in 1 hr = 1/6
Cistern is emptied in 8 hours
Portion of cistern emptied in 1 hr = 1/8
Time taken to fill cistern with both tap and pipe open in 1 hr = 1/6 – 1/8
= 1/24
Therefore, total time taken to fill cistern is reciprocal of 1/24 which is equal to 24 hrs.
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