Population Density

Correct answer: A. Density has increased

Explanation: A quantity increases when its later value is greater than its earlier value. Population density is measured in persons per square kilometre, so the comparison must use the same unit at both times. Here the initial density is 100 and the final density is 125. The units have not changed; only the numerical value has become larger. Therefore, the area has more people per square kilometre than before.

The change can be calculated as \(125-100=25\) persons per square kilometre. Since the difference is positive, density has increased by 25 persons per square kilometre. This supports option A. It has not decreased, remained unchanged, or become zero. A value of 125 cannot represent an unchanged density when the starting value was 100.

Correct answer: B. Density decreased

Explanation: Answer: B, density decreased. Density is being compared at two times or in two situations. The original value is 360 persons per square kilometre and the later value is 300 persons per square kilometre. Since 300 is smaller than 360, the density has gone down. The amount of decrease is 360 − 300 = 60 persons per square kilometre. A is wrong because the final value is not higher. C is wrong because doubling 360 would give 720, not 300. D is wrong because the two values are different. A useful check is to compare the first and final numbers directly before calculating anything else.

Correct answer: A. It helps estimate the need for services and resources

Explanation: Population density helps planners understand how many people and activities are concentrated in a place. A densely populated area may need more housing, roads, public transport, drinking water, drainage, schools, hospitals, and waste-management facilities. A sparsely populated area may require a different arrangement, such as longer service routes or smaller facilities. Density does not describe mountains, rainfall, or sea waves.

Option A is correct because density information supports estimates of demand and helps allocate resources. It does not by itself provide every planning answer, since planners also need information about age, income, settlement form, and future growth. Nevertheless, estimating service and resource requirements is a direct and important use of population-density data.

Correct answer: C. 300 persons per square kilometre

Explanation: Correct answer: C, 300 persons per square kilometre. Population density tells us the average number of people living in one unit of area. The formula is: Population density = Total population ÷ Total area. Here, density = 240,000 ÷ 800 = 300 persons per square kilometre. A quick check is 800 × 300 = 240,000, so the calculation is correct. Option A is wrong because 800 × 200 gives only 160,000. Option B is wrong because 800 × 250 gives 200,000. Option D is wrong because 800 × 400 gives 320,000, which is greater than the given population. Remember: for density, divide population by area and always write the unit persons per square kilometre.

Correct answer: C. The density will remain the same

Explanation: Correct answer: C, the density will remain the same. Population density is the ratio of population to area: D = P ÷ A. Suppose the original population is P and the original area is A. The original density is P/A. After both values double, the new density is 2P ÷ 2A, which simplifies to P/A. Therefore, the ratio does not change. Option A would be correct only if population doubled while area stayed unchanged. Option B would be correct only if area doubled while population stayed unchanged. Option D is incorrect because doubling both numerator and denominator does not multiply a ratio by four. A useful memory cue is: when population and area change by the same factor, density remains unchanged.

Correct answer: A. It will decrease by 25 percent

Explanation: Correct answer: A, the density will decrease by 25 percent. Density is calculated as population divided by area. When the area remains fixed, density changes in exactly the same percentage as population. Let the original population be P and area be A. The original density is P/A. After a 25% decrease, the population becomes 75% of P, so the new density is 0.75P/A, which is 25% lower than the original density. Option B reverses the direction of change. Option C incorrectly doubles the percentage decrease. Option D ignores the fact that fewer people are now distributed over the same area. For example, a density of 400 becomes 300 after a 25% decrease. The key warning is that this equal percentage rule applies here because area does not change.

Correct answer: A. It is more densely populated per unit area

Explanation: Correct answer: A, it is more densely populated per unit area. Density measures the average number of people living in each unit of area. Since 800 persons per square kilometre is greater than 650 persons per square kilometre, the first city has a greater concentration of people on its land. Option B cannot be concluded because total population depends on both density and area; a smaller-area city may have high density but fewer people overall. Option C is also unsupported because density does not tell us which city has the larger area. Option D is wrong because present density alone does not reveal the birth rate; density may also be related to migration, deaths, or the size of the area. The safe interpretation is limited to people per unit area, not every population characteristic.