Dear Reader, Below are three sample pipes problems for your practice.
Question 1
A contractor was engaged to construct a residential complex along with a water tank. The water tank can filled up by Pipe One in 6 hours and by Pipe Two in 8 hours. If the two pipes are opened one after the other each for one hour, how long will it take for the two pipes, pipe One and pipe Two to fill the water tank?
a) 8 hours 20 min b)7 hours 40 min c) 6 hours 45 min d) none of these.
Answer : c) 6 hours 45 min.
Solution :
Pipe one will fill 1/6 of the tank in one hour. Pipe two will fill 1/8 of the tank in one hour.
These pipes are opened one after the other, each run for one hour.
In one turn – that is one hour of pipe one and one hour of pipe two, 1/6 + 1/8 = 7/24 of the tank will be filled in.
So in 6 hours 21/24 of the tank will be filled in and balance will be 3/24 = 1/8 of the tank.
Now in the seventh hour Pipe one will be run. Pipe one can fill 1/6 of the tank in 1 hour or 60 minutes. We can calculate the time taken by Pipe 1 to fill 1/8th of the tank as shown below :
Tank Filled Time Taken 1/6 - 60 min 1/8 - t min
t = 1/8 x 6/1 x 60 = 45 minutes.
So the tank will be filled in 6 hours 45 minutes.
Question 2
SivaChrist constructions constructed a community water tank for Pozhichalur village. The water tank can be filled by Karuna Pipe in 18 hours and Pandian pipe in 24 hours. Karuna Pipe will run for one hour and closed. Pandian pipe will run for the next one hour and closed. This process continues. Which pipe will be running when the tank is filled in fully? How many hours will it take for the tank to be filled in the above process?
a) Pandian, 30 hours 30 min b) Karuna ,10 hours 30 min c) Pandian,5 hours 30 min d) Karuna, 20 hours 30 min
Answer : d) Karuna, 20 hours 30 min
Solution :
Karuna Pipe can fill the tank in 18 hours.
In one hour Karuna Pipe will fill 1/18 of the tank
Pandian Pipe will fill 1/24 of the tank in one hour.
If both the pipes run one after the other once –
1/18 + 1/24 = 7/72 of the tank will be filled.
So, in 20 hours – that after 10 such running - 70/72 of the tank will be filled in and 1/36 of the tank need to be filled in.
Karuna Pipe can fill 1/18th of the tank in 60 minutes. Then the time taken to fill 1/36th of the tank can be calculated as below :
Tank Filled Time Taken 1/18 - 60 min 1/36 - t min
t = 1/36 x 60 x 18 = 30 minutes
So Karuna pipe will be running when the tank is filled in and it will take 20 hours 30 min. for the tank to be filled in completely.
Question 3
Two pipe manufacturers were asked to show demonstration about the performance of their pipes. Pipe X and Pipe Y can fill a tank in four hours. Had they been opened separately Pipe Y will take 6 hours more than Pipe X. How much time will Pipe X take to fill the tank separately?
a) 2 hours b) 1 hour c) 6 hours d) 8 hours
Answer : c) 6 hours.
Solution :
Let the tank be filled in completely by Pipe X in x hours. Therefore in 1 hour, Pipe X will fill 1/x of the tank
Then Pipe Y will take x + 6 hours. Therefore in 1 hour, Pipe Y will fill 1/(x + 6) of the tank.
When Pipe X and Pipe Y are opened together they will take 4 hours to fill the entire tank. In other words, if Pipe X and Pipe Y are opened together for 1 hour, they would had filled 1/4th of the tank. Putting this argument in equation form we get :
1/x + 1/ x+6 = 1/4
x + 6 + x divided by x(x+6) = 1/4
8x + 24 = x2 + 6x
x2 - 2x - 24 = 0
(x-6) (x+4) = 0
So x = 6 (neglecting the negative value of x)