CAT Application of concept of Time and Work in the problems of Pipe and Cistern - Practice Questions & MCQ

Definition: Pipe and cistern problems involve filling or emptying a tank or reservoir. The pipes can either fill (inlet pipes) or empty (outlet pipes) the tank. The 'Time and Work' principles can be directly applied to these problems with the 'work' being represented as the volume of the tank.

Solved Examples:

Pipe A can fill a tank in 6 hours, while Pipe B can empty it in 12 hours. If both pipes are opened simultaneously, in how many hours will the tank be filled completely?

Solution:

1. Identify the Total Work (Volume) (Using Concept 1): Using the LCM method for 6 and 12, we get 12. Let's consider the volume of the tank to be 12 units.

2. Determine 1 Hour Work (Using Concept 2):

   - A’s 1-hour filling = 12 units / 6 hours = 2 units/hour

   - B’s 1-hour emptying = -12 units / 12 hours = -1 unit/hour (The negative sign indicates Pipe B is emptying the tank)

3. Combined 1 Hour Work:

   Combined effect in 1 hour = Pipe A's 1-hour work + Pipe B's 1-hour work = 2 units + (-1 unit) = 1 unit.

4. Calculate Time for Full Tank: 

   To fill 12 units, with a rate of 1 unit/hour, it will take 12 hours.

Tips and Tricks:

1. Visualise with Real-World Analogy: Think of this concept as having taps (pipes) that can fill a bathtub (tank) and drains that can empty it.

2. Categorise Pipes: Always categorise the pipes as either filling or emptying to ensure correct calculations.

3. Be Wary of Impossible Scenarios: If the combined effect of the pipes is to empty the tank, then the tank will never be filled. Always check the net effect before proceeding with time calculations.

Application of Previous Concepts:

- Applying Concept 1 for Total Work (Volume): Determining the volume of the tank is crucial. This is essentially the total work.

- Utilising Concept 2 for 1 Hour Work: Each pipe has an efficiency, i.e., the volume it can fill or empty in a unit time. Calculate this to ascertain their effect on the tank.

- Incorporating Concept 5 for Negative Work: Emptying pipes contribute negatively to the work. Always represent their effect with a negative sign to avoid errors.

The application of 'Time and Work' in pipe and cistern problems makes this topic not only interesting but also an extension of the basic work problems. The same principles apply, but the setting shifts from workers to pipes. Practice remains the cornerstone for mastering these problems.