A boiler tank has 3 pipes, of which 2 are inlet pipes and 1 is for outlet. The inlet pipes can fill the tank in 20 and 30 minutes respectively. The outlet pipe can empty the tank in 60 minutes. If the outlet pipe is turned on for the initial 10 minutes along with both inlet pipes, and then turned off, how long will it take to fill the tank completely, assuming the tank was initially empty?

1. A

   13 minutes

2. B

   14 minutes

3. C

   11 minutes

4. D

   12 minutes

Appeared in: UP NHM CHO 7 Sept 2022(shift-1st)

Explanation

• The problem is solved by breaking it into two phases and calculating the work done in each.
• In the first phase (10 minutes), both inlet pipes and the outlet pipe are active. The net filling rate is (3 + 2 - 1) = 4 units per minute. This fills 40 units of the tank.
• In the second phase, the outlet pipe is closed. The remaining 20 units are filled by the two inlet pipes at a combined rate of (3 + 2) = 5 units per minute.
• The time taken for the second phase is 20 units / 5 units/min = 4 minutes.
• The total time is the sum of the two phases: 10 minutes + 4 minutes = 14 minutes.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. It might arise from a simple arithmetic error during the calculation of time for the second phase.
• Option C: This answer might be obtained if one incorrectly calculates the time for the second phase as 1 minute (10 + 1 = 11). This would imply the remaining capacity was only 5 units, which is wrong.
• Option D: This is a common distractor. A student might calculate the time it would take for only the two inlet pipes to fill the entire 60-unit tank from the beginning (60 units / 5 units/min = 12 minutes), ignoring the initial 10-minute phase with the outlet pipe open.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the concept of 'Pipes and Cisterns', which is a sub-topic of 'Time and Work'. It requires calculating the net rate of work when multiple entities are working simultaneously, some in opposition to others as background academic context rather than a clinical decision trigger.
• This is a general aptitude and reasoning question, not a clinical one.
• Skills in solving such logical problems are tested in nursing entrance exams to assess a candidate's problem-solving abilities and numerical aptitude, which are useful in various non-clinical aspects of nursing management and administration.
• What if? - If the stem changed one defining clue so that 14 minutes no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

• First, identify the question type as a 'Pipes and Cisterns' problem, which is a variation of 'Time and Work'.
• To simplify calculations, determine a hypothetical total capacity for the tank. The best method is to find the Least Common Multiple (LCM) of the individual times given (20, 30, 60).
• Calculate the 'efficiency' or 'rate' of each pipe in 'units per minute'. Assign a positive rate for inlet pipes (filling) and a negative rate for outlet pipes (emptying).
• Divide the problem into distinct phases based on the timeline described. Here, Phase 1 is the first 10 minutes, and Phase 2 is the time after that.
• For each phase, calculate the net rate by summing the rates of all active pipes. Then, calculate the amount of work (units filled) done in that phase.
• Calculate the remaining work (capacity to be filled) after the first phase.

Concept Tested & Keywords

• Concept Tested: This question tests the concept of 'Pipes and Cisterns', which is a sub-topic of 'Time and Work'. It requires calculating the net rate of work when multiple entities are working simultaneously, some in opposition to others.
• Stem keywords: boiler tank, inlet pipes, outlet pipe, fill the tank, empty the tank
• Lead-in keywords: how long

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QkCjQdcA_1fuzHi65iTq_F

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