Concept of Pipes and Cistern
Welcome students to my new blog in aptitude series. In this blog we are going to clear the concept of pipes and cistern. This topic is related to work and wages, I hope you can solve problems on it. Let's revise it.
Lets revise..
There are two kind of pipes, inlet pipe and outlet pipe. Inlet pipe is the pipe that fills the tank or any reservoir and Outlet pipe is the pipe that empties the tank. Mathematically:
- If a pipe fills a tank in 'x' hours, then in one hour it will fill 1/x portion of tank. For e.g, if a pipe takes 4 hours to completely fill a tank of 12 liters, then in 1 hour it will fill 1/4 part of tank, means 3 liters of tank.
- Similarly, If a pipe empties a tank in 'x' hours, then in one hour it will empty 1/x portion of tank. For e.g, if a pipe takes 4 hours to completely empty a tank of 12 liters, then in 1 hour it will empty 1/4 part of tank, means 3 liters of tank.
- If we have inlet and outlet pipes both opened, then in 1 hour part of tank filled/emptied = ∑ (1 / mi) – ∑ (1 / nj). Where,
mi = Time taken by inlet pipe i to fill tank completely.
nj = Time taken by outlet pipe j to empty the tank completely.
Theory part is over. Lets understand this topic with few questions
Que: Two pipes X and Y can fill two tanks in 6 and 8 hours. If both of them are opened together when tank is empty, then how much time it will take to fill tank completely?Solution:
Part of tank filled by X pipe in 1 hour be 1/6.
Part of tank filled by Y pipe in 1 hour be 1/8.
Part of tank filled by pipe X & Y by working together in 1 houe is-
(1/6) + (1/8) = 14/48.
Therefore, 24/7 hours it will take to fill tank completely.
Que:Two inlet pipes work together to fill tank in 24/7 hours. If one outlet pipe Y is attached it then inlet pipes take 20/7 hours to fill tank. What is rate of outlet pipe Y?
Solution:
Inlet pipes rate is 24/7 to fill complete tank.
Hence,
(24/7) - (Y pipe) = (20/7)
(Y pipe) = 4/7 hours.
Therefore, Outlet pipe will work for 4/7 hours.
Practice Questions...
- Three pipes A, B and C are connected to a tank. Out of the three, A is the inlet pipe and B and C are the outlet pipes. If opened separately, A fills the tank in 10 hours, B empties the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill / empty the tank ?
- A cistern has two pipes. Both working together can fill the cistern in 12 minutes. First pipe is 10 minutes faster than the second pipe. How much time would it take to fill the cistern if only second pipe is used ?
- More Problems on Cistern & Pipes.
In closing...
So in this blog we learnt about Pipes and cistern. You observed that pipes concept is similar to work concept. In next blog we will study about Time, Speed & distance. Mail me if you have any query.