Population Density

Density is found by dividing population by area, so the two regions must be compared using the same calculation. For the first region, the result is \(\frac{200000}{500}=400\) persons per square kilometre. For the second region, it is \(\frac{300000}{1000}=300\) persons per square kilometre.

Since 400 is greater than 300, option A, the first region, has the higher density. The second region has more people in total, but it also has twice the area, so its people are less concentrated. This shows why total population alone cannot determine which region is more densely populated.

Population density means the number of people living in one square kilometre. It is found by dividing the total population by the total area. The unit is persons per square kilometre, so the population and area must be used together rather than treating either number as the answer alone.

Here, the population is 500000 and the area is 2500 square kilometres. Therefore, density is \(500000\div2500=200\) persons per square kilometre. Hence, option B is correct. The figure 2500 represents area, not density, while 150, 250 and 500 do not result from the required division.

Arithmetic density is found by dividing population by area. When the population stays constant but the area becomes smaller, the same number of people is counted over fewer square kilometres. Consequently, the ratio must rise. A 20 percent decrease means that the new area is 80 percent of the original area, or \(0.8A\). The new density is therefore \(P/(0.8A)\), which is \(1.25P/A\), or 25 percent higher than before.

Thus option B is correct: density increases. Option A reverses the effect of reducing the denominator. Option C would be possible only if population and area changed in a way that kept their ratio constant, which does not happen here. Option D is impossible because the population remains present and the area does not become zero. The result follows directly from the density formula.

Correct answer: C, 800 square kilometres. The density formula is D = P ÷ A. To find area, rearrange it as A = P ÷ D. Substituting the given values gives A = 256,000 ÷ 320 = 800 square kilometres. A simple calculation is 25,600 ÷ 32 = 800 after cancelling one zero from both numbers. A reverse check confirms the result: density × area = 320 × 800 = 256,000. Option A would give only 192,000 people at the stated density. Option B would give 224,000 people. Option D would give 288,000 people. Thus none of those areas reproduces the given population. Remember that when finding area, divide population by density, not density by population.

Population density tells us how many people live in one square kilometre. To find the total population, multiply the density by the total area. The units also confirm the method: persons per square kilometre multiplied by square kilometres leaves persons. This is a direct application of the meaning of density.

Here, total population is \(1000 \times 120 = 120000\) people. Therefore, option B is correct. Option A is too small, while option D would result from using an unnecessarily large multiplier. The calculation does not require division because both density and area are already given.

Average population density gives one overall figure by dividing the total population of a region by its total area. This is useful for comparison, but it treats the whole area as if people were spread evenly. In reality, settlement is often concentrated near cities, rivers, coasts, transport routes, fertile plains, or other favourable places. Large deserts, mountains, forests, or protected areas may have very few inhabitants.

For example, a country can have a moderate average density even when a small part is extremely crowded and a large part is almost empty. The average hides these internal differences because it combines all places into one number. Therefore, option A is correct. Options B and C are false because the calculation uses both total population and area. Option D is false because average density is a clear numerical measure.

Average density represents the ratio of total population to total area. It does not describe the exact spatial pattern of that population. Two regions can have the same ratio while having very different settlement arrangements: one may contain a few crowded cities and wide empty spaces, while the other may have people spread more evenly.

Thus, option B is correct. Equal areas or equal populations are not required for the key point; what matters is that the population-to-area ratio is equal. Options A, C and D incorrectly treat an average measure as proof of identical distribution.

When the area of a region stays fixed, density changes directly with its population. In-migration means people enter the region from elsewhere. Their arrival increases the total population while the area remains the same, so the number of people per square kilometre rises. This is the most direct factor among the choices.

Therefore, option B, in-migration, is correct. Out-migration removes people and normally lowers density. Population decline has the same downward effect. Expansion of area, if population does not rise proportionately, would generally lower density rather than increase it. The conclusion assumes the incoming population is added to the region.

The question asks for the density after the population changes, so the new population must be used. Population density is calculated by dividing population by area. Here the new population is 100,000 and the unchanged area is 200 square kilometres. Thus, \(D=\frac{100000}{200}=500\) persons per square kilometre.

Therefore, option C is correct. The earlier population of 80,000 is useful only if we want to compare the old density; it gives \(80,000\div200=400\) persons per square kilometre. The increase in population raises density because the available area has not changed. The units are persons per square kilometre, not simply persons or square kilometres.

When the area remains unchanged, population density changes by the same percentage as the population. A decrease of 20 percent means that 80 percent of the original population remains. Since the original density is 400 persons per square kilometre, the new density is \(400\times0.80=320\) persons per square kilometre. Therefore option B is correct.

The same result can be found by calculating the decrease directly. Twenty percent of 400 is \(0.20\times400=80\). Subtracting this decrease from the original density gives \(400-80=320\). The values 300, 340, and 380 do not represent the stated 20 percent reduction. This reasoning works because the area has not changed; if area also changed, the percentage change in density would need another calculation.

Correct answer: C, 300 persons per square kilometre. Because the area is unchanged, a 25% increase in population produces a 25% increase in density. First calculate 25% of 240: 240 × 25/100 = 60. Add this increase to the original density: 240 + 60 = 300 persons per square kilometre. Equivalently, multiply by 1.25: 240 × 1.25 = 300. Option A adds only 30, which is not 25% of 240. Option B adds 40 and is also too small. Option D adds 80, which represents a larger increase than 25%. The important idea is that density follows population proportionally only because area is fixed. A useful shortcut is to remember that 25% means one-fourth; one-fourth of 240 is 60.

The relationship among population, density, and area is density equals population divided by area. Rearranging this gives population equals density multiplied by area. Here the density is 150 persons per square kilometre and the area is 1,600 square kilometres. Therefore population is \(150\times1600=240000\) people, so option B is correct.

The multiplication can be checked as \(15\times16=240\), followed by four zeros from 150 and 1,600, giving 240,000. The units also confirm the result: persons per square kilometre multiplied by square kilometres leaves persons. The other options do not result from the given density and area. No division is needed because population is being found from density and area.

The relationship among population, density, and area is \(Population=Density\times Area\). The given density is 375 persons per square kilometre and the area is 800 square kilometres. Therefore, the total population is \(375\times800\). First calculate \(375\times8=3000\), then multiply by 100 because 800 is 8 hundreds. This gives 300000 people. Hence, option C is correct.

The units also confirm the method: persons per square kilometre multiplied by square kilometres leaves persons. Dividing instead would not produce the required population. A quick check is \(300000\div800=375\), which returns the stated density. The values 250000, 275000, and 325000 would give different densities for the same area, so they do not match the data.

The relationship among population, area, and density is \(D=P/A\). If density and population are known, the area can be found by rearranging this relationship to \(A=P/D\). The units also guide the calculation: persons divided by persons per square kilometre leaves square kilometres.

The population is 350,000 and density is 500 persons per square kilometre. Therefore, \(A=350000\div500=700\) square kilometres. Checking the result, \(700\times500=350000\), which reproduces the given population. Hence option C is correct. The number 500 is a density, not an area, so it must be used as the divisor.

Population density is calculated by dividing population by area: \(D=\frac{P}{A}\). The original population is 200,000 and the original density is 250 persons per square kilometre. Thus the area is \(200000\div250=800\) square kilometres. The question states that this area does not change, so only the population must be replaced in the new calculation.

The new density is \(240000\div800=300\) persons per square kilometre. Hence option B is correct. The increase in population is 40,000, or 20 percent, and because the area stays fixed, density also rises by 20 percent, from 250 to 300. The other choices do not result from the density formula.

Correct answer: B, 150 persons per square kilometre. The original area is found by rearranging density = population ÷ area: area = population ÷ density = 90,000 ÷ 180 = 500 square kilometres. The area then increases by 100, so the new area is 600 square kilometres. Population remains 90,000. Therefore, new density = 90,000 ÷ 600 = 150 persons per square kilometre. Option A would require an area of 750 square kilometres, while option C would require 562.5 square kilometres. Option D is the old density and ignores the increased area. The direction of change also gives a useful check: when the same population is spread over a larger area, density must fall.

Arithmetic density is the number of people divided by the total land area. In this comparison, both regions have the same population, so the numerator is equal. The region with less land has the smaller denominator. Dividing the same number by a smaller positive number produces a larger result, so its arithmetic density will be higher. This conclusion concerns arithmetic density, not necessarily agricultural or physiological density.

Option A is therefore correct. For example, if 100,000 people live in 500 square kilometres, density is 200 persons per square kilometre; in 1,000 square kilometres it is only 100. Option B reverses the mathematical relationship. Option C is wrong because equal population does not ensure equal density when areas differ, and option D ignores that area is essential to the calculation.

A national average density of 250 persons per square kilometre is obtained by dividing the country's total population by its total area. It describes an average for the whole country, not the exact number of residents in every small part of it. Population is usually unevenly distributed: cities, fertile plains, and transport corridors may be crowded, while deserts, mountains, forests, or protected areas may have few residents.

Therefore, option B cannot be concluded with certainty. The statement that the population-to-area ratio is 250, the statement that the average is 250, and the description of density as an average all follow directly from the given information. They do not claim uniform settlement. A national average can remain 250 even when individual square kilometres have values far above or below 250, so exact equality everywhere is the incorrect inference.

To compare densities, calculate population divided by area for each region. For the first region, density is \(\frac{400000}{1600}=250\) persons per square kilometre. For the second region, density is \(\frac{300000}{1000}=300\) persons per square kilometre. Since 300 is greater than 250, the second region has the higher density, so option B is correct.

A larger total population does not automatically mean a higher density. The first region has more people, but it also covers a much larger area. The second region has fewer people overall, yet those people are distributed across a smaller area. This produces more people per square kilometre. Comparing only populations would therefore give the wrong conclusion.

When area remains unchanged, density changes in the same proportion as population because \(Density=\frac{Population}{Area}\). A 10 percent increase in population therefore produces a 10 percent increase in density. Ten percent of the original density 300 is \(0.10\times300=30\). Adding this increase gives \(300+30=330\) persons per square kilometre.

Thus option C is correct. The area of 900 square kilometres is not needed for this shortcut, although it can be used as a check. The original population is \(300\times900=270000\); after a 10 percent increase it is 297,000, and \(297000\div900=330\). Options A and B show smaller increases, while D represents a 20 percent increase.

The relationship among population, area, and density is \(\text{Density}=\frac{\text{Population}}{\text{Area}}\). If density and population are known, the area must therefore be calculated by dividing population by density. The density value of 500 is not itself the area; it tells us how many people live in each square kilometre.

Here, \(\text{Area}=400000\div500=800\) square kilometres. The result can be checked by multiplying density by area: \(500\times800=400000\). Thus 800 square kilometres satisfies all the given information. Therefore, option C is correct; 1,000 would give a population of 500,000 instead.

Correct answer: C, 30 percent. First find the absolute increase: 260 − 200 = 60 persons per square kilometre. Percentage increase is calculated relative to the original value, not the new value: (increase ÷ original density) × 100 = (60 ÷ 200) × 100 = 30%. Option A is incorrect because 20% of 200 is only 40. Option B is incorrect because 25% of 200 is 50. Option D confuses the numerical increase, 60, with a percentage. The denominator must be the original density, 200, because the question asks how much the value increased from its starting point. Memory cue: percentage change = change ÷ original × 100.

Correct answer: B, 25 percent. First calculate the decrease: 400 − 300 = 100 persons per square kilometre. For a percentage decrease, divide the decrease by the original value and multiply by 100: (100 ÷ 400) × 100 = 25%. Option A is wrong because 20% of 400 equals 80. Option C is wrong because 30% of 400 equals 120. Option D is wrong because 40% of 400 equals 160. The number 100 is the absolute decrease, not the percentage decrease. The original density must be used as the reference because the question asks how much the value fell from 400. Memory cue: decrease percentage = decrease ÷ starting value × 100.

A level plain with reliable water is generally favourable for a high population density when other conditions are equal. Flat land makes farming, construction, road building, and settlement easier. Water supports household needs, irrigation, livestock, and many economic activities. Such a region can usually support more people than a place where steep slopes, ice, extreme dryness, or difficult access restrict daily life and production.

Option A is therefore correct. An ice-covered plateau has severe limits on habitation and agriculture. An extremely arid desert lacks dependable water, while an inaccessible mountain slope creates difficulties for transport, construction, and cultivation. These places may have settlements, but their average density is usually lower under the stated condition. The word “if” is important: real density also depends on technology, jobs, history, and infrastructure. The supplied answer is consistent.

Employment-based in-migration means that people move into a city to obtain jobs. If many workers and their families arrive while the city boundary or built-up area changes little, more people are living within nearly the same space. The population-to-area ratio therefore rises, producing higher density.

Option A is correct because job opportunities are a strong human factor shaping settlement and concentration. Out-migration would usually reduce the number of residents, while industrial closure would remove jobs and may encourage people to leave. A collapsed transport network would generally weaken accessibility rather than attract a rapid population increase.