SGPGI Nursing Officer…: If 36 doctors check 140 patients in 14 hours, then how many doctors need to see these patients in 7 hours?

SGPGI Nursing Officer-2023

Non Nursing Subjects

Medium

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).

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.

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

Qv0SPWBcRM4UKb2b7xwiep