Q3. Pipes and Cisterns

A pipe is connected to a tank or cistern. It is used to fill or empty the cistern. The amount of work done by a pipe is a part of the tank filled or emptied in unit time.

Three pipes A, B and C are connected to a tank. A and B fill the tank in 6 hours and 8 hours respectively when operated independently. Pipe C empty the full tank in 12 hours when opened alone



Based on the above information, answer the following questions:

(i) If both pipes A and B are opened together, then the tank can be filled in

(a)4 2/3 hours
(b) 3 3/7 hours
(c) 3 3/4 hours
(d) 2 4/5 hours

(ii) If pipes A and C are opened together, then the tank can be filled in

(a) 12 hours
(b) 16 hours
(c) 20 hours
(d) 24 hours

(iii) If pipes B and C are opened together, then the tank can be filled in

(a) 12 hours
(b) 16 hours
(c) 20 hours
(d) 24 hours

(iv) If all three pipes A, B and C are opened together, then the tank can be filled in

(a) 4.2 hours
(b) 4.6 hours
(c) 4.8 hours
(d) 5 hours

(v) If all three pipes are opened together, then the tank is filled in 24 hours. If pipe C can empty the tank at the rate of 20 litres/hours, then the capacity of the tank is

(a) 40 litres
(b) 60 litres
(c) 80 litres
 (d) 90 litres

Solution