Formulas For Pipes & Cisterns

Questions for Pipes and Cisterns:

Question 1:  Tarun and Varun started a game in which they checked whose pipe fills the tank faster Tarun’s pipe A and  Varun’ s pipe B can fill a cistern in 6 hours and 8 hours, respectively. If both pipes are opened simultaneously, how long will they take to fill the cistern?

         Answer:

Let the total capacity of the cistern be C (considering 1 unit of capacity).

The filling rate of Pipe A = 1/6 (fraction of the cistern filled per hour). The filling rate of Pipe B = 1/8 (fraction of the cistern filled per hour).

When both pipes are opened simultaneously, their filling rates are additive:

Combined filling rate = (1/6) + (1/8) = 7/24 (fraction of the cistern filled per hour).

Now, to find the time it will take to fill the cistern, we use the formula:

Time = 1 / Combined filling rate

Time = 1 / (7/24) = 24 / 7 ≈ 3.43 hours

Hence They will take approximately 3 hours and 26 minutes to fill the cistern when both pipes A and B are opened simultaneously.

Question 2: A tank has been connected to three pipes such that Pipe A can fill it in 4 hours, Pipe B in 6 hours, and Pipe C can empty it in 8 hours. If all pipes are opened at the same time, how long will it take to fill the tank wholly ?

Answer:

 Let the total capacity of the cistern be C (considering 1 unit of capacity).

The filling rate of Pipe A = 1/4 (fraction of the tank filled per hour).

The filling rate of Pipe B = 1/6 (fraction of the tank filled per hour).

The emptying rate of Pipe C = -1/8

All three pipes are opened simultaneously, their net filling rate is the sum of the filling rates of Pipes A and B and the emptying rate of Pipe C:

Net filling rate = (1/4) + (1/6) + (-1/8) = 12/48 + 8/48 – 6/48 = 14/48 (fraction of the tank filled per hour).

Now, to find the time it will take to fill the tank, we use the formula:

Time = 1 / Net filling rate

Time = 1 / (14/48) = 48 / 14 ≈ 3.43 hours

Hence, It will take approximately 3 hours and 26 minutes to fill the tank completely when all three pipes A, B, and C are opened simultaneously

Question 3: Rajat and Raghav took two pipes Pipe A which can fill a cistern in 12 hours, and Pipe B  which can empty the cistern in 15 hours. If both pipes are opened together, how long will it take to fill the cistern?

Answer:
Let the total capacity of the cistern be C (considering 1 unit of capacity).

The filling rate of Pipe A = 1/12 (fraction of the cistern filled per hour). The emptying rate of Pipe B = -1/15 (negative value since it is emptying, and we consider emptying as a negative filling rate).

When both pipes are opened simultaneously, their net filling rate is the sum of the filling rate of Pipe A and the emptying rate of Pipe B:

Net filling rate = (1/12) + (-1/15) = 5/60 – 4/60 = 1/60 (fraction of the cistern filled per hour).

Now, to find the time it will take to fill the cistern, we use the formula:

Time = 1 / Net filling rate

Time = 1 / (1/60) = 60 hours

Hence,  It will take 60 hours to fill the cistern when both pipes A and B are opened simultaneously.