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Question
Two taps can fill a cistern in 10 hours and 8 hours respectively. A third tap can empty it in 15 hours. How long will it take to fill the empty cistern, if all of them are opened together?
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Solution
First tap can fill a cistern in 10 hours
Second tap can fill the cistern in 8 hours
Third tap can empty the cistern in 15 hours
∴ First tap's 1 hour's work = `1/10`
Second tap's 1 hour's work = `1/8`
and third tap's 1 hour's work = `1/15`
If all of them are opened together, then
heir one hour's work = `1/10 + 1/8 - 1/15`
`= (12 + 15 - 8)/120 = (27 - 8)/120 = 19/120`
∴ They can fill the cistren in =`120/19` hours
`= 6 6/19` hours
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