Two taps can fill a cistern in 3 hours and 21 hours respectively. A third tap can empty it in 3 hours. How long (in hours) will it take to fill two-third of the empty cistern, if all of them are opened together?3970

1. A

   42

2. B

   56

3. C

   14

4. D

   28

Appeared in: RRB Nsg. Superintendent-2026 (Shift -1st)

Explanation

• The rate of the first filling tap is 1/3 of the cistern per hour.
• The rate of the second filling tap is 1/21 of the cistern per hour.
• The rate of the emptying tap is -1/3 of the cistern per hour.
• The net combined rate is the sum of the individual rates: (1/3) + (1/21) - (1/3) = 1/21 of the cistern per hour.
• The time required to fill a fraction of the cistern is calculated as (Fraction of Work) / (Net Rate).
• Time to fill 2/3 of the cistern = (2/3) / (1/21) = (2/3) × 21 = 14 hours.

Why Other Options Were Wrong

• Option A: This is the time it would take to fill two full cisterns. The time to fill one full cistern is 21 hours, so 2 × 21 = 42 hours.
• Option B: This value does not correspond to a logical misinterpretation of the problem's parameters and is likely included as a distractor to catch arithmetic errors.
• Option D: This is the time it would take to fill 4/3 of the cistern (one full cistern and one-third more). Calculation: (4/3) × 21 = 28 hours.

Related Visual

• Visual 1: Flowchart - Illustrates the rates of the two inlet taps (+1/3 and +1/21) and one outlet tap (-1/3), showing how the net rate is calculated by summing the positive rates and subtracting the negative rate, resulting in a net fill rate of +1/21 per hour.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time: Pipes and Cisterns as background academic context rather than a clinical decision trigger.
• This type of problem tests quantitative aptitude, a skill often required for competitive nursing entrance examinations.
• The underlying concept of calculating net rates (inflow vs. outflow) is analogous to calculating a patient's fluid balance (Intake vs. Output) in a clinical setting, which is a critical nursing skill for monitoring hydration and kidney function.
• What if? If the third tap also filled the cistern in 3 hours instead of emptying it, the net rate would be 1/3 + 1/21 + 1/3 = 7/21 + 1/21 + 7/21 = 15/21 = 5/7 per hour. The time to fill 2/3 would be (2/3) / (5/7) = 14/15 hours, which is approximately 56 minutes.

How to Approach the Question

• First, identify the rate of work for each tap. The rate is the reciprocal of the time taken (Rate = 1/Time).
• Assign a positive sign (+) to the rates of taps that fill the cistern and a negative sign (-) to taps that empty it.
• Calculate the combined (net) rate by summing the individual rates of all taps.
• Determine the total amount of work to be done, which in this case is filling 2/3 of the cistern.
• Use the formula: Time = Work to be Done / Net Rate.
• Substitute the values and solve for the time. Ensure your units are consistent.

Concept Tested & Keywords

• Concept Tested: Work and Time: Pipes and Cisterns
• Stem keywords: taps, fill a cistern, 3 hours, 21 hours, empty, two-third
• Lead-in keywords: How long

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