Below are practice questions dealing with Pipes.
Question 1
Mr. Pugazh Vendhan, a building contractor was approached by Sumanth Apartments for constructing a new water tank and installation of pipes for filling up the same. Mr. Pugazh Vendhan made a study of the complex and fitted with Pipe A and Pipe B. Pipe A can fill the tank fully in 16 hours and Pipe B can fill the tank fully in 24 hours. Pipe A and Pipe B run together for 8 hours. Thereafter Pipe A was shut and Pipe B alone was used. How many hours more would Pipe B take to fill the tank fully?
a) 3 hours b) 4 hours c) 6 hours d) 8 hours
Answer : b) 4 hours.
Solution :
Pipe A can fill the tank fully in 16 hours.
In one hour Pipe A will fill 1/16 of the tank.
Similarly Pipe B will fill in one hour 1/24 of the tank.
The two pipes run for 8 hours.
So in 8 hours Pipe A and Pipe B will fill
( 1/16 + 1/24) 8 = (5/48 ) x 8 = 5/6 of the tank.
1/6 of the tank is to be filled in by Pipe B
hour portion of tank that can be filled 1 1/24 ? 1/6
Pipe B can fill in 1 hour 1/24 of tank
1/6 of the tank will be filled in 1/6 x 24/1 = 4 hours.
Question 2
Velavan and Company are experts in providing plumbing facilities. They were approached for construction of a community water tank in Oragadam. Velavan and Company built a huge water tank and fitted it with three pipes named Cauvery, Ganga and Godavari . Pipes Ganga, Cauvery and Godavari can fill the community water tank in 30 hours, 25 hours and 40 hours respectively. In order to see that all the pipes are put into use equally, the Chairman of Oragadam Municipality advised the operator to run the Pipes Ganga, Cauvery and Godavari one after the other i.e. each pipe to be run for one hour each. Viz. Ganga will run for one hour followed by Cauvery for one hour and Godavari for one hour. Again the cycle will be repeated like this. When will the tank be filled fully i.e. during the running of Ganga or Cauvery or Godavari ?
a) Ganga, 33rd hour b) Ganga, 31st hour
c) Cauvery, 33rd hour d) Cauvery, 32nd hour
Answer : b) Ganga, 31st hour
Solution :
Ganga can fill the tank in 30 hours. In one hour it can fill 1/30th part of tank.
Cauvery can fill the tank in 25 hours. In one hour it can fill 1/25th part of tank.
Godavari can fill the tank in 40 hours. In one hour it can fill 1/40th part of tank.
Ganga, Cauvery and Godavari, when they run for one hour each (totally 3 hours)
(1/30 + 1/25 + 1/40 ) of the tank will be filled in.
= 59/600 of the tank will be filled in three hours
So in 30 hours 590/600 of the tank will be filled in.
Portion of tank unfilled after 30 hours would be 1 - 590/600 = 1/60
1/60 of the tank will be left unfilled after 30 hours.
During 31st hour Ganga is capable of filling 1/30 of the tank.
But since 1/30 is greater than that of the remaining tank portion 1/60, Ganga will be filling the tank during 31st hour comfortably.
Question 3
Anjali Plumbing Company has two pipes –Pipe X and Pipe Y – these pipes can fill a tank in 37 ½ minutes and 45 minutes respectively. Both pipes are opened. The tank will be filled in just 30 minutes, if the pipe Y is turned off after ___ .
a) 10 min b) 5 min c) 9 min d) 15 min
Answer : c) 9 min.
Solution :
Pipe X can fill the full tank in 37 ½ = 75/2 minutes . Therefore in one minute it can fill 1/(75/2 ) = 2/75th portion of tank.
Pipe Y can fill the full tank in 45 minutes. Therefore in one minute it can fill 1/45th portion of tank.
Let Pipe Y be turned off after x minutes
Both the pipes would be running for the first x minutes, and then pipe Y alone will run for the remaining (30 - x) minutes.
Then Part filled in by (pipe X + pipe Y) in x min + part filled in pipe Y in (30-x) min = 1 (as you would be knowing1 represents full tank)
Therefore ( 2/75 + 1/45)x + (30- x) 2/75 = 1
11x /225 + (60 - 2x) / 75 = 1
11x + 180 - 6x = 225
x = 9 min.