There are 7 pipes attached with a tank out of which some are inlets and some are outlets. Every inlet can fill the tank in 10 h and every outlet can empty the tank in 15 h. When all the pipes are opened simultaneously, the tank is filled up in 2 8/ 11 h. Find the numbers of inlets and outlets.?

Let number of outlets be x
∴ Number of inlets = ( 7 - x )
Time taken to fill the tank when all the pipes are opened = 30/11h
Part of tank filled in 1 h when all the pipes are opened = 11/30 h
According to the question,
(7 - x)/10 - x/15 = 11/30
⇒ {3(7 - x) - 2x}/30 = 11/30
⇒ 21 - 3x - 2x = 11
⇒ 5x = 10
∴ x = 2
Hence, number of outlets = 2 and number of inlets = 7 - 2 = 5