A camp has provisions for 52 persons for 16 days. In how many days, will the same provisions finish off if the strength of the camp is increased to 104 persons?

Appeared in: Bihar NHM CHO-2025

Explanation

This problem demonstrates an inverse relationship: as the number of people increases, the number of days the provisions last must decrease.
The total amount of provisions can be thought of as 'person-days', which is a constant. Initially, this is 52 persons × 16 days = 832 person-days.
To find the new number of days (D₂), we divide the total person-days by the new number of people: 832 person-days / 104 persons = 8 days.
The formula for this inverse proportion is M₁ × D₁ = M₂ × D₂, where M is the number of men (persons) and D is the number of days.
Substituting the values: 52 × 16 = 104 × D₂, which simplifies to 832 = 104 × D₂, so D₂ = 8.

Option B: This is a calculation error. The result of (52 × 16) / 104 is exactly 8, not 7.
Option C: This value is incorrect. An increase in people should lead to a decrease in days, not a smaller decrease. 11 days is too long.
Option D: This is a calculation error. The result of (52 × 16) / 104 is exactly 8, not 6.

Visual 1: Infographic: A balance scale showing '52 persons' and '16 days' on one side, and '104 persons' and '?' on the other, visually representing the inverse relationship where doubling the people halves the days.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Inverse Proportion as background academic context rather than a clinical decision trigger.
This type of question tests logical reasoning and basic mathematical skills, which are essential for nurses in various calculations, such as medication dosage, IV drip rates, and resource management.
Accurate calculation is a critical patient safety skill. A small math error can have significant consequences in a clinical setting.
What if the number of people was halved to 26 instead of doubled? The provisions would last twice as long. Using the formula: 52 × 16 = 26 × D₂, so D₂ = (52 × 16) / 26 = 32 days.

How to Approach the Question

First, identify the quantities involved in the problem: number of persons and number of days for provisions.
Determine the relationship between these quantities. As the number of people increases, the food will last for fewer days. This is an inverse proportion.
Recall the formula for inverse proportion: M₁ × D₁ = M₂ × D₂.
Assign the given values to the variables in the formula: M₁ = 52, D₁ = 16, M₂ = 104.
Solve the equation for the unknown variable, D₂.
Check your answer for logical consistency. Since the number of people doubled, the number of days should be halved (16 / 2 = 8), which confirms the calculation.

Concept Tested & Keywords

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Practise the full Bihar NHM CHO-2025

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