Pipe A and Pipe B can fill an empty tank in 45 minutes and 63 minutes respectively, while Pipe C can empty a full tank in 54 minutes. When the tank was empty, initially both inlet pipes (A and B) were opened. After some time, Pipe B was closed and at the same time Pipe C was opened. The tank was filled completely in a total of 75 minutes from the start. For how many minutes was Pipe B kept open?

Appeared in: UP NHM CHO 7 Sept 2022 (Shift-2)

Explanation

The problem requires calculating the duration a specific pipe was open in a multi-stage filling and emptying process.
The solution involves finding a common unit of work (total capacity) by calculating the LCM of the individual times.
Efficiencies (work rate per minute) are calculated for each pipe; filling pipes have positive rates, and emptying pipes have negative rates.
An equation is formed by summing the work done by each pipe over its respective operational time, equating the total to the tank's capacity.
Solving the linear equation for the unknown time 't' gives the duration Pipe B was open.

Option B: This value is incorrect. If Pipe B were open for 20 minutes, the total volume filled would be 525 + (65 * 20) = 525 + 1300 = 1825 units, which is less than the required 1890 units. This likely results from a minor calculation error.
Option C: This value is incorrect. If Pipe B were open for 22 minutes, the total volume filled would be 525 + (65 * 22) = 525 + 1430 = 1955 units, which is more than the tank's capacity of 1890 units.
Option D: This value is significantly incorrect. If Pipe B were open for 16 minutes, the total volume filled would be 525 + (65 * 16) = 525 + 1040 = 1565 units, which is far short of the required 1890 units.

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 quantitative aptitude, specifically the ability to solve problems related to work and time.
While not directly a clinical skill, strong analytical and problem-solving abilities are crucial for nurses in various aspects of their job, including medication dosage calculations, managing fluid balances, and interpreting patient data.
This type of logical reasoning is a component of many nursing entrance and competitive examinations in India.

How to Approach the Question

First, identify the rates of work for each pipe. Note that filling pipes have a positive rate and emptying pipes have a negative rate.
To simplify calculations, find a common 'total work' unit by calculating the Least Common Multiple (LCM) of the given time periods. This represents the tank's capacity.
Calculate the efficiency (work per minute) for each pipe by dividing the total capacity by the time each pipe takes.
Define a variable (e.g., 't') for the unknown quantity, which is the time Pipe B was open.
Construct an equation representing the total work done. Sum the work of each pipe (efficiency multiplied by its operating time). The total must equal the tank's capacity.
Solve the algebraic equation for 't' to find the answer.

Concept Tested & Keywords

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Practise the full UP NHM CHO 7 Sept 2022 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.