Pipe P can fill a tank in 12 minutes, pipe Q can fill the tank in 18 minutes, and pipe R can empty a full tank in 36 minutes. If all these pipes are opened simultaneously, find the time taken to fill the empty tank.

1. A

   5 minutes

2. B

   9 minutes

3. C

   11 minutes

4. D

   7 minutes

Appeared in: NHM UP Staff Nurse-2023 Shift-2nd

Explanation

• The problem is solved by calculating the net rate of work done by all three pipes together.
• Pipes filling the tank have a positive rate of work (1/12 and 1/18 of the tank per minute), while the emptying pipe has a negative rate (-1/36 of the tank per minute).
• The combined rate is the sum of the individual rates: (1/12 + 1/18 - 1/36), which simplifies to 1/9 of the tank per minute.
• The total time to fill the tank is the reciprocal of the combined rate, which is 1 divided by (1/9), resulting in 9 minutes.

Why Other Options Were Wrong

• Option A: This time is incorrect. A time of 5 minutes would imply a combined filling rate of 1/5 of the tank per minute, which is significantly faster than the actual calculated rate of 1/9.
• Option C: This time is incorrect. A time of 11 minutes suggests a slower filling rate (1/11 of the tank per minute), underestimating the combined efficiency of the pipes.
• Option D: This time is incorrect. A time of 7 minutes would require a combined rate of 1/7 of the tank per minute, which is faster than the actual rate achieved by the pipes working together.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time problems involving pipes and cisterns as background academic context rather than a clinical decision trigger.
• This is a general aptitude question, not directly related to clinical nursing practice.
• Strong numeracy and problem-solving skills are essential for nurses for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data charts accurately.
• What if Pipe R was also a filling pipe? If Pipe R filled the tank in 36 minutes instead of emptying it, the combined rate would be (1/12 + 1/18 + 1/36) = (3+2+1)/36 = 6/36 = 1/6. The tank would then fill in 6 minutes.

How to Approach the Question

• First, identify the task: find the total time to fill a tank with multiple pipes working together.
• Represent the rate of each pipe as the fraction of the tank it can fill or empty in one unit of time (in this case, one minute).
• Assign a positive sign (+) to the rates of pipes that fill the tank and a negative sign (-) to the rate of the pipe that empties it.
• Calculate the net or combined rate by adding the individual rates.
• The total time required to fill the tank is the reciprocal of this combined rate (Time = 1 / Net Rate).
• Check the final calculated time against the given options to select the correct answer.

Concept Tested & Keywords

• Concept Tested: Work and Time problems involving pipes and cisterns.
• Stem keywords: Pipe P, Pipe Q, Pipe R, fill, empty, simultaneously
• Lead-in keywords: find the time taken

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QU6ZAbt7Agt2rNM8bOkMCy

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