Question

A cistern has two inlets A and B which can fill it in 12 hours and 15 hours respectively. An outlet can empty the full cistern in 10 hours. If all the three pipes are opened together in the empty cistern, how much time will they take to fill the cistern completely? (2 marks)

Answer 1

Inlet A can fill the cistern in = 12 hours

Inlet A can fill the cistern in 1 hour = 1/12

Inlet B can fill the cistern in = 15 hours

Inlet B can fill the cistern in 1 hour = 1/15

Outlet pipe can empty the cistern in = 10 hours

Outlet pipe can empty the cistern in 1 hour = 1/10
(1 mark)

So we have, (1/12 + 1/15) – 1/10

= (9/60) – 1/10

= (9-6)/60

= 3/60

= 1/20 part

∴ When all 3 pipes are opened together to empty the cistern, time taken to fill the cistern completly = 1/(1/20) = 20 hours
(1 mark)