With decreasing population, the man-land ratio

Concept

In this exam convention, the man–land ratio means usable or habitable land available per person: R = L / P, where L is land area and P is population.

With land area fixed, this ratio varies inversely with population. It is the reciprocal direction of population density, which is P / L.

Application

1. Let the original population be P and fixed land area be L, so the original man–land ratio is R = L / P.

2. After population decreases to P′, with P′ < P and the same L, the new ratio is R′ = L / P′.

3. For positive quantities, dividing the same numerator L by the smaller denominator P′ gives a larger value, so R′ > R and the man–land ratio increases.

Cross-check and contrast

For example, 10 km2 shared by 100 people gives 0.10 km2 per person. The same 10 km2 shared by 80 people gives 0.125 km2 per person, confirming an increase.

• Decreases describes population density P / L, which is the reciprocal of the exam-convention man–land measure L / P. With fixed land, P / L becomes smaller when population falls.

• Remains constant would require population to stay unchanged or land to change in the same proportion as population.

• More than one and None of the above do not supply another possible direction for one before-and-after quotient comparison.

Result

Therefore, the man–land ratio increases.