In a hospital, the ratio of nurses to doctors is 7:2. If there are 210 nurses, how many doctors are working in the hospital?

Appeared in: RML Lucknow - 2021

Explanation

The given ratio of nurses to doctors is 7:2, which establishes a proportional relationship.
The number of nurses is given as 210. This corresponds to the '7' part of the ratio.
First, find the value of one 'part' by dividing the number of nurses by their share of the ratio: 210 ÷ 7 = 30.
Then, calculate the number of doctors by multiplying this value by their share of the ratio: 30 × 2 = 60.

Option A: This value (30) is the common multiplier found by dividing 210 by 7. It represents one 'part' of the ratio, not the total number of doctors.
Option C: This result (90) would be obtained if the ratio of nurses to doctors was 7:3, as 30 (the multiplier) times 3 equals 90.
Option D: This number does not logically follow from the given 7:2 ratio and the number of nurses. It's a calculation error.

Clinical Relevance

Nursing practice connection: Knowing Solving ratio and proportion problems helps nurses interpret findings accurately and avoid errors in routine assessment, medication administration, and patient teaching.
While this is a math question, understanding ratios is crucial in healthcare for nurse-to-patient staffing, ensuring patient safety and quality of care.
Ratios are also fundamental for medication dosage calculations, where a small error can have significant consequences.
What if? If the hospital needed to maintain a 4:1 nurse-to-doctor ratio with the same 210 nurses, the number of doctors would be (210 / 4) = 52.5. Since you can't have half a doctor, this highlights how ratios guide staffing decisions and may require hiring adjustments.

How to Approach the Question

First, identify the key information provided: the ratio (nurses to doctors is 7:2) and the known quantity (210 nurses).
Recognize that the question is asking for the unknown quantity (number of doctors).
Set up a proportion. You can express the ratio as a fraction: (Nurses / Doctors) = 7 / 2.
Substitute the known value into the proportion: 210 / Doctors = 7 / 2.
Solve for the unknown variable. You can cross-multiply: 7 × Doctors = 210 × 2.
Calculate the final answer: Doctors = 420 / 7 = 60. Then, match your result with the given options.

Concept Tested & Keywords

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