Population Density

Correct answer: B. 267 persons per square kilometre

Explanation: When people move out and the area does not change, first subtract the people who left from the original population. The new population is \(270000-30000=240000\). The area remains 900 square kilometres, so the new density is \(240000\div900=266.666\ldots\) persons per square kilometre. Rounded to the nearest whole person, this is about 267. Therefore, option B is correct.

The original density was 300 persons per square kilometre because \(270000\div900=300\). The population loss is spread across 900 square kilometres, reducing density by \(30000\div900=33.33\), giving \(266.67\). Option C is the old density and ignores the out-migration, while 250 and 333 do not follow from the calculation. The approximate wording justifies rounding to 267.

Correct answer: C. 350 persons per square kilometre

Explanation: Population density means the number of people living in one unit of area. When more people settle in the same region, the population increases, but the area does not change. Therefore, the density rises. The relevant relationship is \(\text{Density}=\frac{\text{Population}}{\text{Area}}\), and the area must remain in square kilometres.

The new population is \(180000+30000=210000\). The area is still 600 square kilometres, so the new density is \(\frac{210000}{600}=350\) persons per square kilometre. Thus, option C is correct. The value 300 is the original density before the additional people arrived, while 400 is not obtained from the given figures.

Correct answer: B. 200 persons per square kilometre

Explanation: Density changes when population or area changes. First find the unchanged population from the original density and area: population = density × area = 150 × 2,000 = 300,000 people. The question says that this population stays constant while the area becomes 1,500 square kilometres.

Now divide the same population by the new area: new density = 300,000 ÷ 1,500 = 200 persons per square kilometre. The density rises because the same number of people is now spread over a smaller area. Thus option B is correct. The result is not 225 or 250, since those would require a still smaller area or a larger population.

Correct answer: B. 264 persons per square kilometre

Explanation: The given density and area first allow us to find the original population. Population equals density multiplied by area, so the original population is \(240\times500=120,000\). When 12,000 people are added, the new population becomes 132,000. The area has not changed, so only the numerator in the density calculation changes.

Now divide the new population by the unchanged area: \(132000\div500=264\). The new density is therefore 264 persons per square kilometre, making option B correct. Adding 12,000 directly to 240 would mix population and density units and is not valid. Option C would also imply a larger increase than the stated population change.

Correct answer: C. 292 persons per square kilometre

Explanation: Density is the number of people living in each unit of area. The original population is 210,000 and the original density is 350 people per square kilometre. Since density equals population divided by area, the original area can be found by reversing the formula. This gives an area of 600 square kilometres. The population then falls by 35,000, leaving 175,000 people.

The new density is \(\frac{175000}{600}=291.666\ldots\) people per square kilometre. Rounded to the nearest whole number, this is 292 persons per square kilometre. Therefore option C is correct. Option D would be too high, because the area has not changed while the population has decreased. The supplied calculation and mapping are accurate.

Correct answer: A. Housing and infrastructure

Explanation: Very high average density means that many people live in a limited amount of land. Planning authorities must provide enough homes, roads, public transport, drinking water, drainage, electricity, schools, hospitals and waste-management services for this large concentration of people. If supply does not keep pace with demand, overcrowding, congestion and pressure on basic services may develop.

Therefore, option A is correct because housing and infrastructure are directly affected by population concentration. Ocean-depth measurement, mountain-height surveys and longitude calculations may be useful for particular scientific or mapping tasks, but they are not the main planning pressure created by high population density.

Correct answer: B. It is an average that can hide local extremes

Explanation: National average density uses the whole country: total population divided by total land area. The entire desert is included in the area even if almost nobody lives there. At the same time, a few cities may contain many people in very small spaces. Combining these very different places into one calculation produces a single average, not a detailed picture of settlement patterns.

Therefore, option B is correct: the national average can hide local extremes. It may appear moderate even when cities are extremely crowded and the desert is nearly empty. It does not show only city density, and it does not ignore the desert; both contribute to the national calculation. Option A is wrong because an average cannot fully display internal variation.

Correct answer: C. 360 persons per square kilometre

Explanation: A 10 percent population decrease leaves 90 percent of the original population. The new population is therefore \(160{,}000\times0.90=144{,}000\). The area does not change, so it remains 400 square kilometres. New density is calculated as \(\frac{144{,}000}{400}=360\) persons per square kilometre.

Thus option C is correct. Another quick way is to note that density also falls by 10 percent when area stays fixed: \(400\times0.90=360\). Option A is not the result of a 10 percent reduction, and B and D represent smaller or different changes. The original density of 400 is reduced because the same land area now supports fewer people. The supplied answer and calculation are accurate.

Correct answer: A. Because it indicates the concentration of people per unit area

Explanation: Arithmetic population density measures the average number of people living in each unit of total area. It is useful as an initial indicator because a high concentration of people may place greater demand on housing land, roads, water, sanitation, schools, and other services. It can therefore suggest pressure on available space and resources, although it does not measure the actual quantity or quality of every resource.

Option A is correct because it states exactly what density indicates: people per unit area. Option B is wrong because density does not directly tell us how much water, land, or fuel exists. Options C and D are unrelated consequences and use absolute language. Density should be interpreted with resource availability, technology, income, and local conditions rather than treated as a complete measure of carrying capacity.

Correct answer: C. 240 persons per square kilometre

Explanation: Population density measures the average number of people living in one unit of area. The formula is \(Population\ density = \frac{Population}{Area}\). Here the population is 216,000 and the area is 900 square kilometres. Dividing gives \(216000 \div 900 = 240\), so the average density is 240 persons per square kilometre.

Option C is correct because it has the result with the required unit. The calculation can also be checked by noting that 900 multiplied by 240 equals 216,000. Option A is too low, while B and D do not result from the stated division. This is an average for the whole region; it does not mean that every square kilometre contains exactly 240 people. Therefore C is the correct choice.

Correct answer: B. 135000

Explanation: When density and area are known, total population is obtained by multiplying them: \(P=D\times A\). In this case, \(D=180\) persons per square kilometre and \(A=750\) square kilometres. Thus, \(P=180\times750=135000\) persons. The square-kilometre unit in density cancels with the square-kilometre area, leaving people as the final unit.

Option B is correct. A quick calculation is \(180\times(75\times10)=13,500\times10=135,000\). Dividing density by area would be the wrong operation and would not produce a population value. Option A is 15,000 too low, option C is 15,000 too high, and option D is 45,000 too high. The multiplication formula directly determines the answer.

Correct answer: C. 900 square kilometres

Explanation: The relationship among population, density, and area is \(Population=Density\times Area\). Rearranging it gives \(Area=\frac{Population}{Density}\). Substituting the values, \(Area=\frac{144000}{160}\). Since \(160\times900=144000\), the area is 900 square kilometres.

Therefore option C is correct. The units also support the calculation: persons divided by persons per square kilometre leaves square kilometres. Multiplying density by population would be incorrect because that would not produce an area. The values 720, 800, and 960 do not satisfy the original relationship; for example, an area of 800 would give only 128,000 people at density 160. Hence the supplied answer is clear and consistent.

Correct answer: A. Region A

Explanation: Population density has an inverse relationship with area when population is held constant. In symbols, density is population divided by area. Region A has the same population as Region B but only 75% of B’s area, because its area is 25% smaller. Therefore its density is population divided by a smaller denominator. More precisely, if B’s density is D, A’s density is D / 0.75, or about 1.33D. Thus A’s density is roughly one-third higher than B’s.

Option A is correct. The comparison does not require the actual population or actual areas; the percentage relationship is enough. Option B would be possible only if B had the smaller area, and option C would require equal areas. Option D is unnecessary because the information given determines the result completely. The key reasoning is that concentrating an equal number of people in less land increases the number of people per unit area.

Correct answer: A. X has 40 percent more population

Explanation: Density is population divided by area. If two regions have exactly the same area, their population sizes change in the same proportion as their densities. Thus, comparing their densities is enough to compare their populations; the common area does not distort the comparison.

Let Region Y have population \(P\) and area \(A\). Its density is \(P/A\). If Region X has density 40% more, its density is \(1.4(P/A)\). Since X also has area \(A\), its population is \(1.4P\), or 40% more than Y's. It is not twice as large. Therefore, option A is correct.

Correct answer: B. It will increase by about 18.2 percent

Explanation: Population density is a ratio, so its change depends on both population and area. If the original population is \(P\) and area is \(A\), the original density is \(P/A\). A 30% population increase makes population \(1.3P\), while a 10% area increase makes area \(1.1A\). Thus the new density is \(\frac{1.3P}{1.1A}=1.1818\frac{P}{A}\).

The new density is therefore about 118.18% of the old density. The increase is \(118.18-100=18.18\%\), approximately 18.2%. Hence option B is correct. Simply subtracting 10% from 30% would give 20%, but that shortcut ignores that the changed area is in the denominator and does not give the exact ratio.

Correct answer: C. Density will remain unchanged

Explanation: Density is the ratio of population to area. If both population and area are reduced by the same percentage, their ratio does not change. A 15 percent decrease leaves 85 percent of each original value. Thus the new density is \(0.85P/0.85A\), and the common factor 0.85 cancels. The relationship between people and space remains exactly the same.

For instance, suppose population is 850 and area is 100 square kilometres. The density is 8.5. After a 15 percent decrease, population is 722.5 and area is 85 square kilometres. The new density is \(722.5/85=8.5\). Therefore, option C, density remains unchanged, is correct. It would decrease only if population fell proportionally more than area.

Correct answer: C. 1.75 times

Explanation: Population density is calculated as population divided by area. If the original population is \(P\) and area is \(A\), the original density is \(P\div A\). A 40% population increase makes the population \(1.4P\), while a 20% area decrease makes the area \(0.8A\). The new density is therefore \(1.4P\div0.8A = 1.75(P\div A)\).

Thus, the new density is 1.75 times the original density. Both changes raise density: there are more people and less area. Option C is correct. It is not enough to add 40% and 20% as ordinary percentage changes; the area change affects the denominator, so division by 0.8 is essential. This produces 1.75, not 1.4, 1.5, or 2 times.

Correct answer: A. 60 percent

Explanation: Density equals population divided by area. A decrease of 25 percent leaves 75 percent of the original population, while an increase of 25 percent makes the area 125 percent of its original value. The new density must therefore account for both changes rather than considering only the population change.

Let the original density be \(P/A\). The new density is \(0.75P\div1.25A=(0.75/1.25)(P/A)=0.6(P/A)\). Thus, the new density is 60 percent of the original density, so option A is correct. Simply adding or subtracting the two percentages would be wrong because the population and area affect density through division, not by direct addition.

Correct answer: B. 300,000

Explanation: Correct answer: B, 300,000 people. The relationship among population, density, and area is density = population ÷ area. Rearranging gives population = density × area. Therefore, population = 480 × 625 = 300,000. One convenient method is 625 × 48 = 30,000, followed by multiplying by 10 to obtain 625 × 480 = 300,000. Option A is too small; 480 × 625 is not 250,000. Option C would result from an incorrect multiplication. Option D is also greater than the correct product. A reverse check confirms the answer: 300,000 ÷ 625 = 480 persons per square kilometre. The final answer is a total number of people, so it should not be expressed in persons per square kilometre; that unit belongs to density.

Correct answer: C. 300 persons per square kilometre

Explanation: Population density tells us how many people live, on average, in one square kilometre. It is found by dividing the total population by the total area. The unit is persons per square kilometre, so both the population and the area must be used in the stated units. This measure allows regions of different sizes to be compared fairly.

Here, density is \(198000 \div 660\). Since \(660 \times 300=198000\), the quotient is 300 persons per square kilometre. Therefore, option C is correct. A value such as 330 would result from an incorrect division and does not reproduce the given population when multiplied by 660.

Correct answer: B. 1200 square kilometres

Explanation: Population density is the number of people living per unit of area. When population and density are known, area is found by dividing the total population by the population in each square kilometre. This is the inverse of the formula \(Population=Density\times Area\), so the units also confirm the method.

Substitute the values: \(Area=270000\div225\). Since \(225\times1200=270000\), the area is 1200 square kilometres. Thus option B is correct. Dividing by 225 rather than multiplying is essential; multiplication would produce a quantity much larger than the stated population and would not have the correct area interpretation.

Correct answer: B. 150 persons per square kilometre

Explanation: Population density changes when the number of people changes, while the area remains the same. First find the population left after migration. From 320,000 people, 80,000 leave, so the remaining population is \(320000-80000=240000\). The area is still 1,600 square kilometres because no change in area is mentioned.

Now apply the density formula: \(\text{density}=\text{population}/\text{area}=240000/1600\). Dividing both numbers gives 150 persons per square kilometre. Therefore, option B is correct. The original density was 200 persons per square kilometre, and the decrease to 150 is reasonable because out-migration reduces population without reducing the area.

Correct answer: C. 250 persons per square kilometre

Explanation: Population density is found by dividing the number of people by the area they occupy. When people migrate into a region, its population increases. If the area does not change, the new density must also rise because more people are living in the same space.

The new population is \(180000+45000=225000\). The area remains 900 square kilometres, so the new density is \(225000\div900=250\) persons per square kilometre. Thus option C is correct. The value 200 is the original density, while 225 would not be obtained by simply adding the number of migrants to the old density.

Correct answer: B. 480 persons per square kilometre

Explanation: Population density tells us how many people live in one unit of area. It is calculated by dividing the total population by the total area. When the population stays fixed but the area becomes larger, the same people are spread over more land, so the density becomes lower. The correct choice is B, 480 persons per square kilometre.

Use the formula \(\text{density}=\frac{\text{population}}{\text{area}}\). Thus, \(\frac{240000}{500}=480\) persons per square kilometre. The earlier density was \(\frac{240000}{400}=600\), so the increase in area reduced the density from 600 to 480. Choice A uses the wrong division, while choice D is the old density, not the new one.

Correct answer: B. 300 persons per square kilometre

Explanation: When population stays constant, density changes inversely with area. An area increase of 20 percent means the new area is \(1.20A\), not just \(0.20A\). Therefore, the new density is \(P/(1.20A)\), which equals the old density divided by 1.2. More area is now available for the same number of people, so the density must fall.

Using the given value, the calculation is \(360/1.2=300\) persons per square kilometre. Equivalently, if the original area were 100 units, the new area would be 120 units and the same population would be distributed across those 120 units. Hence option B is correct. The value 432 would result from multiplying by 1.2, which is inappropriate when population is fixed.