Two pipes A and B can fill a tank separately in 2 hours and 6 hours respectively. If both the pipes are opened simultaneously then how much time will it take to fill the empty tank?

1. A

   1 hour 30 minute

2. B

   2 hour 30 minute

3. C

   1 hour 15 minute

4. D

   1 hour 10 minute

Appeared in: SGPGI Nursing Officer-2024

Explanation

• The core principle is to calculate the work rate of each pipe as a fraction of the tank filled per hour.
• Pipe A's rate is 1/2 tank per hour, and Pipe B's rate is 1/6 tank per hour.
• When working together, their rates are added: (1/2) + (1/6) = (3/6) + (1/6) = 4/6 = 2/3 tank per hour.
• The total time is the reciprocal of the combined rate: 1 / (2/3) = 3/2 hours.
• Converting 3/2 hours (or 1.5 hours) to minutes gives 1 hour and 30 minutes.

Why Other Options Were Wrong

• Option B: This answer overestimates the time required. A logical check is that the combined time must be less than the time taken by the fastest pipe alone (which is 2 hours). 2 hours and 30 minutes is longer than 2 hours.
• Option C: This answer (1.25 hours) results from an incorrect calculation of the combined fractional rates. It does not correspond to the reciprocal of (1/2 + 1/6).
• Option D: This answer (approximately 1.17 hours) is also a result of miscalculation and does not match the correct time of 1.5 hours.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time and Work (Pipes and Cisterns) as background academic context rather than a clinical decision trigger.
• While this is a general aptitude question, the underlying skill of calculating rates is crucial in nursing.
• Nurses frequently calculate IV drip rates (gtt/min), medication infusion rates (mL/hr), and fluid balance over time, which all rely on the same 'rate-time-volume' principles.
• What if? If Pipe B was an outlet pipe that emptied the tank in 6 hours, the combined rate would be (1/2) - (1/6) = 1/3 tank per hour, and it would take 3 hours to fill the tank.

How to Approach the Question

• First, identify the 'work' to be done, which is filling 1 tank.
• Next, determine the rate of each individual pipe. The rate is always the reciprocal of the time taken (Rate = 1 / Time).
• If the pipes are working together to fill, add their individual rates to get the combined rate.
• The total time taken to complete the work together is the reciprocal of the combined rate (Time = 1 / Combined Rate).
• Finally, convert the time from a fraction of an hour into hours and minutes for the final answer.

Concept Tested & Keywords

• Concept Tested: Time and Work (Pipes and Cisterns)
• Stem keywords: pipes, fill a tank, simultaneously, time
• Lead-in keywords: how much time

Question ID

Q78Lo460c9V5oEibkTLg_9

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