A tap can fill a tank in 7 hours and an outlet pipe can empty it in 8 hours. If both the tap and the pipe are opened simultaneously, how long will it take to fill the tank?

1. A

   56 hours

2. B

   52 hours

3. C

   50 hours

4. D

   54 hours

Appeared in: NHM UP Staff Nurse-2023 shift 1st

Explanation

• The rate of the filling tap is calculated as the reciprocal of the time it takes to fill the tank, which is 1/7 of the tank per hour.
• The rate of the emptying pipe is 1/8 of the tank per hour.
• When both are open, the work rates are opposing. The net rate of filling is the difference between the filling rate and the emptying rate.
• Net Rate = (1/7) - (1/8) = (8 - 7) / 56 = 1/56 of the tank per hour.
• The total time to fill the tank is the reciprocal of the net rate, which is 1 / (1/56) = 56 hours.

Why Other Options Were Wrong

• Option B: This is an incorrect calculation. It does not correspond to the correct formula for calculating the net rate of work.
• Option C: This is an incorrect calculation. It does not correspond to the correct formula for calculating the net rate of work.
• Option D: This is an incorrect calculation. It does not correspond to the correct formula for calculating the net rate of work.

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: Pipes and Cisterns as background academic context rather than a clinical decision trigger.
• This question tests general aptitude and problem-solving skills, which are essential for nurses in making quick, logical decisions.
• The underlying principle of calculating net rates is analogous to fluid balance calculations in clinical practice. Nurses must accurately track fluid intake (IV fluids, oral intake) versus fluid output (urine, drains, emesis) to determine a patient's net fluid status.
• What if? If both were filling taps (one in 7 hours, one in 8 hours), their rates would add up. The combined rate would be (1/7) + (1/8) = 15/56 tank/hour, and the time to fill would be much faster, at 56/15 hours (approximately 3.73 hours).

How to Approach the Question

• First, identify the type of question. This is a mathematical problem involving work, rate, and time, specifically for pipes and cisterns.
• Determine the rate of work for each component. The rate is the reciprocal of the time taken (Work Rate = 1 / Time).
• Assign a positive sign to the rate for filling (inlet) and a negative sign for emptying (outlet).
• Calculate the combined or net rate of work by adding the individual rates. In this case, it's (1/7) - (1/8).
• The total time required to fill the tank is the reciprocal of the net rate.
• Perform the calculation carefully and match the result with the given options.

Concept Tested & Keywords

• Concept Tested: Work and Time: Pipes and Cisterns
• Stem keywords: tap, fill, tank, outlet pipe, empty, simultaneously
• Lead-in keywords: how long

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QfoTZYv2sMT0YEmePTPv_E

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