A cistern can be filled by two pipes a and b in 10 and 15 hours respectively and is then empited by a tap in 8 hours.If all the taps are opened,then cistern will be fill in how many hours?

Pipe ‘a’ fills the cistern in 10 hours, so in 1 hour the part of cistern filled by pipe a= 1/10

Pipe ‘b’ fills the csitern in 15 hours, so in 1 hour the part of cistern filled by pipe b= 1/15

A tap can empty the cistern in 8 hours, so in 1 hour the part of cistern emptied by tap = 1/8

Now if we open all the pipes and taps, then the cistern is filled in 1 hour = (1/10 + 1/15 – 1/8) = (5/120) = 1/24 part

Hence, in 1 hour 1/24 part of cistern is filled.

Therefore, in 24 hours the cistern is completely filled.

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