Population Density

Correct answer: B. Displacement of low-income households may decrease

Explanation: Answer: B. Affordable housing reduces the cost barrier that often prevents lower-income households from living in central areas. If suitable homes remain available, these households may continue to live near jobs, schools, hospitals, and transport. This can reduce displacement caused by rising rents or land values and may preserve a socially mixed residential pattern. A is incorrect because successful affordable housing does not reserve the centre only for high-income residents. C is incorrect because housing prices and availability directly influence where people can live. D is incorrect because the policy primarily affects residential access, although it may indirectly influence land use. Memory cue: housing policy changes who can access a place, not merely what buildings are used for.

Correct answer: B. Health risks may reduce settlement concentration despite agricultural advantages

Explanation: Direct answer: B. Fertile land and adequate rainfall are favourable for agriculture because they can support crops and livelihoods. However, widespread tropical diseases may reduce the attractiveness and productivity of the area. Illness can affect household well-being, workers’ ability to work, costs of treatment, and people’s willingness to settle permanently. As a result, population may be less concentrated than the agricultural conditions alone would suggest. A is wrong because agricultural fertility does not remove health risks. C is wrong because rainfall is helpful only within suitable environmental and social conditions; it does not always increase population. D is wrong because disease environments can influence mortality, migration, productivity, and settlement decisions. The answer does not claim that the region must be empty; it states that health risks may weaken the expected concentration. Memory cue: favourable land can attract people, but unhealthy environments can repel them.

Correct answer: C. Some workers may move from expensive cities to the region

Explanation: Direct answer: C. Traditionally, many people lived close to their workplaces because daily commuting was necessary. Reliable high-speed internet can weaken that link for jobs that can be performed remotely. If housing is affordable and the region also has basic services, safety and reasonable connectivity, some workers may move from expensive cities while continuing to work for distant employers. Option A is wrong because remote areas may gain residents under suitable conditions. B is wrong because digital connectivity can influence employment location and settlement decisions. D is wrong because remote work allows some people to earn from jobs located elsewhere. This does not mean every worker will move: family needs, service quality and the nature of the job still matter. Memory cue: digital connectivity can separate the place of work from the place of residence.

Correct answer: D. Reduced hazard risk may support population retention and further investment

Explanation: Direct answer: D. A storm-surge barrier is a form of hazard-reduction infrastructure. By lowering the expected exposure of homes, businesses and transport systems to coastal flooding, it may make residents more willing to remain and investors more willing to maintain or expand activity. This can support population retention and possibly further concentration, provided that the protection is effective and other urban services remain adequate. Option A is wrong because protection does not necessarily push people away. B is wrong because the effects can include housing, business and migration decisions, not just tourism. C is wrong because elevation is one physical factor, not the sole determinant. The important caution is that a barrier reduces risk; it does not remove every coastal hazard or guarantee population growth.

Correct answer: C. 460 persons per square kilometre

Explanation: Population density means the average number of people living in one square kilometre. To find it, divide the population by the area. Since the area does not change, any percentage increase in population produces the same percentage increase in density. This is an important condition because density depends on both population and area.

The original density is \(480000 \div 1200=400\) persons per square kilometre. A 15% increase means the new population is \(480000\times1.15=552000\). Therefore, the new density is \(552000\div1200=460\) persons per square kilometre. Equivalently, \(400\times1.15=460\). Thus option C is correct; 480 would represent a 20% increase over the original density, not 15%.

Correct answer: B. 280 persons per square kilometre

Explanation: Population density is calculated by dividing total population by area. First find the original population: \(320\times750=240000\) people. When 30,000 people leave, the remaining population is \(240000-30000=210000\). The area does not change, so divide the remaining population by 750: \(210000\div750=280\) persons per square kilometre.

Therefore, option B is correct. A common mistake is to subtract 30,000 directly from the density, but people and density have different units. Another mistake is to change the area after migration; the question states that people leave, not that the region’s area changes. The new density is consequently 280 persons per square kilometre.

Correct answer: C. 360000 people

Explanation: First calculate region A's density using \(D=\frac{P}{A}\): \(D_A=\frac{240000}{600}=400\) persons per square kilometre. The question says both regions have equal density, so region B must also have a density of 400 persons per square kilometre. Its population is therefore \(P_B=D_B\times A_B=400\times900=360000\) people.

Hence, option C is correct. The population is larger in B because its area is larger while density remains equal. Option B might seem possible if one overlooked the change from 600 to 900 square kilometres, but equal density means population must increase in the same proportion as area. The calculation confirms 360,000 people.

Correct answer: C. Increase by 50 percent

Explanation: Density is found by dividing population by area. Let the original population be \(P\) and the original area be \(A\). After the changes, population is \(1.2P\), while area is \(0.8A\). The new density is therefore \(\frac{1.2P}{0.8A}=1.5\frac{P}{A}\). It becomes 1.5 times the original density.

An increase to 1.5 times the original value means an increase of 0.5 times, or 50 percent. Simply adding 20 percent and 20 percent gives 40 percent, but that ignores the fact that area is in the denominator and has decreased. The correct result is therefore option C, an approximate 50 percent increase.

Correct answer: B. 82 percent

Explanation: Density means population divided by area. Let the original population be \(P\) and the original area be \(A\). The original density is \(P/A=450\) persons per square kilometre. A 10 percent population decrease gives \(0.9P\), while a 10 percent area increase gives \(1.1A\).

The new density is therefore \(\frac{0.9P}{1.1A}=\frac{0.9}{1.1}\frac{P}{A}\), which is about \(0.818\) of the old density. Expressed as a percentage, this is about 81.8 percent, normally rounded to 82 percent. Therefore option B follows. The value 90 percent ignores the simultaneous increase in area.

Correct answer: C. 400 persons per square kilometre

Explanation: First find the population and area that remain in the original region after the separation. The new population is \(360000-40000=320000\) people because 40,000 people are removed. The new area is \(900-100=800\) square kilometres because 100 square kilometres form the separate unit. The required density is therefore \(\frac{320000}{800}=400\) persons per square kilometre.

Option C matches this result. It is important to subtract both quantities before dividing; using the original population or original area would describe the old region, not the changed one. The result is also reasonable because the removed population and area have been specified together, and the remaining region has 320,000 people across 800 square kilometres. Hence C is correct.

Correct answer: C. Higher than 200

Explanation: Total population density is calculated using the whole land area, including land where nobody lives. If 40 percent of the country is uninhabited, the population is concentrated on the remaining 60 percent. The same population is therefore spread over a smaller denominator when inhabited-land density is calculated.

For example, suppose the total area is 100 square kilometres and the population is 20,000. Overall density is 200 persons per square kilometre. If people live on only 60 square kilometres, the inhabited-area density is about 333.3 persons per square kilometre, which is higher than 200. Hence option C is correct. The exact value is not required to establish the direction of comparison.

Correct answer: C. 400 persons per square kilometre

Explanation: Correct answer: C, 400 persons per square kilometre. Arithmetic density means total population divided by the total geographical area. Let the total area be A square kilometres. The population is therefore 300A. Only 75% of the area is habitable, so the habitable area is 0.75A. Because the population does not change and all of it occupies the smaller habitable area, the new density is 300A ÷ 0.75A = 300 ÷ 0.75 = 400 persons per square kilometre. A is wrong because it does not apply the full area reduction. B is wrong because it simply adds 25% to 300; density does not increase by the percentage of unusable land in that way. C correctly divides by the remaining area. D is too high and has no correct calculation behind it. Memory cue: with fixed population, a smaller effective area produces a higher density.

Correct answer: B. Distribution may differ despite equal density

Explanation: Arithmetic density is an average for the whole region. It is found by dividing total population by total area, so it gives no information about the internal pattern of settlement. Two regions can have the same average even when one has people concentrated in a few large cities and the other has people spread more evenly across villages and towns.

Hence, option B is correct. Equal arithmetic density does not mean equal spatial distribution. The first region does not necessarily have a higher density, and the second does not necessarily have a smaller population. To understand internal concentration, we would need more detailed information such as settlement maps, population by subregion, or measures of urban concentration.

Correct answer: B. 1833 persons per square kilometre

Explanation: Population density is calculated by dividing population by area. The original population is 600,000 and the original area is 300 square kilometres. A 10 percent population increase gives \(600000\times1.10=660000\). A 20 percent area increase gives \(300\times1.20=360\) square kilometres. The new density is therefore \(\frac{660000}{360}=1833.33\) persons per square kilometre.

Rounding to the nearest whole person gives about 1,833 persons per square kilometre, so option B is the matching choice. It is important to apply each percentage to the correct original quantity before dividing. The density does not remain 2,000 because population and area do not rise by the same percentage: area rises faster than population, causing the average number of people per square kilometre to fall.

Correct answer: B. 400 persons per square kilometre

Explanation: Let the original area be \(A\) and population be \(P\). The original density is \(\frac{P}{A}=500\). A 25 percent increase makes the new area \(1.25A\), while population remains \(P\). The new density is therefore \(\frac{P}{1.25A}=\frac{500}{1.25}=400\) persons per square kilometre. Increasing area without adding people spreads the same population over more space.

Thus, option B is correct. The density falls, but it does not fall by simply subtracting 25 percent from 500; the denominator is multiplied by 1.25. Option A, 375, would represent a different calculation. The reciprocal factor is important: a 25 percent larger area makes the density 80 percent of the old value, which is 400.

Correct answer: C. 450 persons per square kilometre

Explanation: Density is calculated by dividing population by area. When population stays unchanged and area becomes smaller, the same number of people is concentrated in less space. The density must therefore rise. A reduction of 20 percent does not mean subtracting 20 percent directly from the original density, because the denominator changes.

Let the original area be A. After a 20 percent reduction, the new area is \(0.8A\). The original density is 360 persons per square kilometre, so the unchanged population is \(360A\). The new density is \(\frac{360A}{0.8A}=\frac{360}{0.8}=450\) persons per square kilometre. Hence option C is correct. The value 432 comes from an incorrect direct percentage adjustment.

Correct answer: C. 327 persons per square kilometre

Explanation: For a changed population density, both new population and new area must be calculated first. It would be incorrect to use the original density or to add the population increase without also updating the area. Density is always the final population divided by the final area.

The new population is \(420000+70000=490000\). The new area is \(1400+100=1500\) square kilometres. Therefore, \(\text{Density}=\frac{490000}{1500}=326.67\) persons per square kilometre. Rounded to the nearest whole person, this is 327. Hence option C is correct. The value 320 is not the result of the required division.

Correct answer: C. 313 persons per square kilometre

Explanation: Correct answer: C, approximately 313 persons per square kilometre. Density equals population divided by area, so both percentage changes must be included. A 30% population increase multiplies population by 1.30, while a 4% area increase multiplies area by 1.04. Thus new density = 250 × 1.30 ÷ 1.04 = 250 × 1.25 = 312.5, which rounds to approximately 313. A, 288, is too low and does not follow the correct ratio of the two changes. B, 300, does not reflect the stated changes accurately. D, 325, effectively gives too much importance to the population increase and neglects the area increase. The important rule is to use multiplication factors, not to add or subtract percentage changes directly from density.

Correct answer: B. 587 persons per square kilometre

Explanation: Density changes according to the relative changes in population and area, not according to either percentage alone. A population decline of 12 percent leaves 88 percent of the original population, so its factor is \(0.88\). An area decline of 10 percent leaves 90 percent of the original area, giving a factor of \(0.90\).

Starting with density 600, the new value is \(600\times\frac{0.88}{0.90}=586.67\) persons per square kilometre, which rounds to about 587. The population falls slightly more, proportionally, than the area, so density decreases but does not fall by the full 12 percent. Therefore option B is correct; 573 would incorrectly apply the population reduction directly to density.

Correct answer: C. 308 persons per square kilometre

Explanation: First find the original population using \(Population=Density\times Area\). It is \(280\times1500=420000\) people. The population then increases by 42,000, so the new population is \(420000+42000=462000\). Because the area stays 1,500 square kilometres, the new density is \(\frac{462000}{1500}=308\) persons per square kilometre.

Thus option C is correct. A quick check is useful: an increase of 42,000 people over 1,500 square kilometres adds \(42000\div1500=28\) persons per square kilometre. Adding 28 to the original density 280 gives 308. Options A, B, and D do not reflect this exact increase and would imply different population changes.

Correct answer: B. 437.5 persons per square kilometre

Explanation: Population density is calculated by dividing population by area. First, the original area must be found because the question gives the original population and density. The original population is 350,000 and the original density is 500 persons per square kilometre. When the population stays unchanged but the area becomes larger, the density must become lower.

Original area = \(350000 \div 500 = 700\) square kilometres. After an increase of 100 square kilometres, the new area is \(700 + 100 = 800\) square kilometres. The new density is therefore \(350000 \div 800 = 437.5\) persons per square kilometre. Hence option B is correct. A value such as 500 would ignore the increase in area.

Correct answer: C. 500 persons per square kilometre

Explanation: The stated density of 400 persons per square kilometre is based on the entire area. If 20 percent is uninhabitable, only the remaining 80 percent can support the population. Removing part of the denominator while keeping the same population makes the density on usable land higher than the overall density.

Let total area be A. The population is \(400A\), and usable area is \(0.8A\). Thus effective density is \(400A/(0.8A)=500\) persons per square kilometre. Therefore, option C is correct. The value is not 480 because the usable area is 80 percent, so the original density must be divided by 0.8, not multiplied by it.

Correct answer: B. Second by 100

Explanation: Density must be calculated separately for each region. For the first region, divide 600,000 people by 1,500 square kilometres: \(600000/1500=400\) persons per square kilometre. For the second, divide 450,000 people by 900 square kilometres: \(450000/900=500\) persons per square kilometre. Comparing the results shows that the second region is more densely populated.

The difference is \(500-400=100\) persons per square kilometre. Therefore option B, “the second by 100,” is correct. A larger population does not automatically mean a higher density, because area must also be considered. The first region has more people, but it occupies much more land; the second has fewer people concentrated in a smaller area, producing the higher density.

Correct answer: C. 240 persons per square kilometre

Explanation: The original population is density multiplied by area: \(250\times1600=400000\). After a 20 percent population increase, population becomes \(400000\times1.20\). After a 25 percent area increase, area becomes \(1600\times1.25\). It is simpler to compare density factors: new density equals old density multiplied by \(1.20\div1.25=0.96\). Thus \(250\times0.96=240\) persons per square kilometre, so C is correct.

Although population rises, area rises by a larger percentage. The denominator therefore grows faster than the numerator, causing density to fall by 4 percent. The exact new values are 480,000 people and 2,000 square kilometres, and \(480000\div2000=240\). This also shows why simply adding 20 percent to density would be wrong: the area change must be included.

Correct answer: B. 450 persons per square kilometre

Explanation: Density changes according to both population and area. The original density is 480 persons per square kilometre. A 25 percent population decrease leaves 75 percent of the original population, or a factor of 0.75. A 20 percent area decrease leaves 80 percent of the original area, or a factor of 0.80. The new density factor is therefore 0.75/0.80=0.9375.

The new density is 480×0.9375=450 persons per square kilometre. It falls because population decreases proportionally more than area. Thus option B is correct. Simply subtracting 25 percent from 480 would give 360, but that ignores the simultaneous reduction in area. Likewise, subtracting 20 percent from the density is not valid, because density is a ratio and both parts of that ratio have changed.