SGPGI Nursing Officer-2023
Non Nursing Subjects
Medium
If 36 doctors check 140 patients in 14 hours, then how many doctors need to see these patients in 7 hours?
Appeared in: SGPGI Nursing Officer-2023
Explanation
- This is a classic work-rate problem where the total amount of work (checking 140 patients) is constant.
- The relationship between the number of doctors and the time taken is one of inverse proportion: if you decrease the time, you must increase the number of doctors proportionally.
- The formula for this relationship is: (Number of doctors₁) × (Time₁) = (Number of doctors₂) × (Time₂).
- Plugging in the given values: 36 doctors × 14 hours = ? doctors × 7 hours.
- Solving for the unknown: (36 × 14) / 7 = 72 doctors.
- Since the time is halved (from 14 hours to 7 hours), the number of doctors required must be doubled (36 × 2 = 72).
Why Other Options Were Wrong
- Option A: This is an incorrect calculation. This number of doctors would only provide 64 × 7 = 448 doctor-hours, which is insufficient to complete the required work of 504 doctor-hours.
- Option C: This incorrectly assumes the number of doctors doesn't change when the time is halved. This would result in only half the work being done (36 × 7 = 252 doctor-hours).
- Option D: This is a very small number and would result in only 3 × 7 = 21 doctor-hours, which is far from the required 504 doctor-hours needed to check all the patients.
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 mathematical concept of inverse proportion, specifically in the context of work-rate problems as background academic context rather than a clinical decision trigger.
- This type of calculation is fundamental for hospital administration and nursing management when creating staff rosters to ensure adequate patient coverage.
- Proper staffing based on patient load (acuity and number) and available time is critical for patient safety and quality of care.
- What if? If the number of patients doubled to 280, and the time was still 7 hours, you would need to double the workforce again. The initial work for 140 patients was 504 doctor-hours. For 280 patients, it would be 1008 doctor-hours. In 7 hours, this would require 1008 / 7 = 144 doctors.
How to Approach the Question
- First, identify the type of problem. This is a work-rate question where the total work is constant.
- Next, identify the variables involved: number of doctors, number of patients, and time in hours.
- Recognize that the number of patients (140) is the same in both scenarios, meaning the total work required is constant.
- Understand the relationship between the remaining variables: the number of doctors and the time taken are inversely proportional. As one decreases, the other must increase.
- Set up the equation for inverse proportion: M₁ × T₁ = M₂ × T₂ (where M=Men/Doctors, T=Time).
- Substitute the known values (M₁=36, T₁=14, T₂=7) into the equation and solve for the unknown variable (M₂).
Concept Tested & Keywords
- Concept Tested: This question tests the mathematical concept of inverse proportion, specifically in the context of work-rate problems.
- Stem keywords: doctors, patients, hours, how many
- Lead-in keywords: how many
Question ID
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