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?

Answer 1

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