A pipe can fill a tank in 15 hours. Due to a leak in the bottom, it is filled in 20 hours. If the tank is full, how much time will the leak take to empty it?

1. A

   60 hours

2. B

   55 hours

3. C

   54 hours

4. D

   56 hours

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

• The filling pipe's work rate is 1/15 of the tank per hour.
• The combined rate of the filling pipe and the leak is 1/20 of the tank per hour.
• The leak's work rate is the difference between the pipe's rate and the combined rate: 1/15 - 1/20.
• This difference calculates to 1/60, which means the leak empties 1/60th of the tank per hour.
• Therefore, the total time for the leak to empty the tank is the reciprocal of its rate, which is 60 hours.

Why Other Options Were Wrong

• Option B: This is an incorrect result. It does not follow from the correct calculation of the difference in work rates (1/15 - 1/20).
• Option C: This is an incorrect result, likely stemming from a miscalculation of the least common multiple (LCM) or an error in the fractional subtraction.
• Option D: This is a mathematically incorrect answer based on the provided data and the work-rate formula.

Related Visual

• Visual 1: Diagram - A simple diagram of a water tank. Show an inlet pipe at the top labeled 'Fills in 15 hrs' and an outlet leak at the bottom labeled 'Empties in 't' hrs'. This helps visualize the opposing actions and the net effect on the water level.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work-rate problems involving pipes and cisterns as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude and logical reasoning, which are foundational skills for problem-solving.
• While not directly clinical, the ability to analyze rates and variables is analogous to monitoring patient vitals over time or calculating medication dosages, which require precision and logical thinking.
• What if the leak caused the tank to fill in 30 hours instead of 20? The leak's rate would be 1/15 - 1/30 = 1/30, meaning it would take 30 hours to empty the tank. This shows that a slower net fill time implies a more significant leak.

How to Approach the Question

• First, identify the knowns: Time for the pipe to fill the tank (15 hours) and the time for the tank to fill with the leak (20 hours).
• Convert these times into 'work rates'. The rate is the reciprocal of the time (e.g., rate = 1/time). The unit will be 'tank per hour'.
• Recognize that the net filling rate (with the leak) is the difference between the pipe's filling rate and the leak's emptying rate.
• Set up the equation: Rate(Pipe) - Rate(Leak) = Net Rate. Let 't' be the time the leak takes to empty the tank, so its rate is 1/t.
• The equation becomes: 1/15 - 1/t = 1/20.
• Solve this algebraic equation for 't' by isolating the term 1/t and then finding the reciprocal.

Concept Tested & Keywords

• Concept Tested: Work-rate problems involving pipes and cisterns
• Stem keywords: pipe, fill, tank, leak, empty
• Lead-in keywords: how much time

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QKcxLONERNOTiMeSCQDSTv

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