5 pipes can fill a tank in 10 hours and 10 cisterns can empty it in 6 hours. If one pipe and one cistern is opened and the rest are closed, then the tank is filled in ______ hours.

1. A

   150

2. B

   300

3. C

   200

4. D

   250

Appeared in: DSSSB October 2024

Explanation

• The problem requires finding the net rate of work when a filling pipe and an emptying cistern operate simultaneously.
• The rate of one pipe is 1/50 of the tank per hour, and the rate of one cistern is 1/60 of the tank per hour.
• The net filling rate is the difference: (1/50) - (1/60) = (6-5)/300 = 1/300 of the tank per hour.
• The total time to fill the tank is the reciprocal of the net rate, which is 1 / (1/300) = 300 hours.

Why Other Options Were Wrong

• Option A: This value is incorrect. It does not correspond to the calculated net filling rate of 1/300 per hour.
• Option C: This value is incorrect. It does not match the calculated time of 300 hours based on the net rate.
• Option D: This value is incorrect. It likely arises from an arithmetic error during the subtraction of fractions or finding the common denominator.

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 (Pipes and Cisterns) as background academic context rather than a clinical decision trigger.
• This question tests foundational mathematical and logical reasoning skills, which are crucial for nurses.
• Nurses frequently perform calculations for medication dosages, IV drip rates, and fluid balance, all of which require precision and an understanding of rates over time.
• Accurate calculation skills are a cornerstone of patient safety, preventing medication errors and ensuring treatments are administered correctly.

How to Approach the Question

• First, identify the individual work rates. Calculate the time it takes for a single pipe to fill the tank and a single cistern to empty it.
• Convert these times into rates (i.e., the fraction of the tank filled or emptied per hour). The rate is the reciprocal of the time (1/time).
• Determine the net effect. Since one component is filling and the other is emptying, subtract the emptying rate from the filling rate.
• Calculate the final net rate. This tells you what fraction of the tank is filled per hour when both are active.
• Finally, find the total time by taking the reciprocal of the net rate. If the net rate is 1/X, the total time is X hours.

Concept Tested & Keywords

• Concept Tested: Work and Time Problems (Pipes and Cisterns)
• Stem keywords: pipes, fill, tank, hours, cisterns, empty
• Lead-in keywords: filled in

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