Population Density

Correct answer: A. Area may also be increasing in the same proportion as population

Explanation: Arithmetic population density is the ratio of total population to total area, written as D=P/A. If the population increases while the ratio remains unchanged, the denominator must increase in the same proportion. For instance, if population doubles and area also doubles, the quotient remains the same. Thus an expanding administrative boundary or an increase in the measured area could allow total population to rise without changing average density.

Option A describes this mathematically possible situation. If the area shrank, density would normally rise rather than remain stable when population was increasing, so option B is unsuitable. Option C contradicts the statement that population is increasing, and option D is false because area is essential to the density formula. In a real country, area does not usually expand quickly, but the question asks what is possible, including a changed measurement boundary.

Correct answer: B. Density will decrease

Explanation: Density is a ratio of population to area, so changing the area while holding population constant changes the ratio. If a city’s administrative boundary expands, the measured area becomes larger. The same number of residents is then spread across a larger denominator, so the calculated average density falls. This is a change in the statistical boundary, even if no person moves and the physical settlement pattern remains exactly the same.

Option B is correct. In symbols, with fixed population P, changing area from A to a larger value A' gives \(P/A' < P/A\). Density would increase only if population rose sufficiently while the area expanded, and it would remain unchanged only if population and area rose in the same proportion. Therefore A, C, and D do not follow from the stated conditions.

Correct answer: C. Because an average can hide differences between dense and sparse areas

Explanation: National arithmetic density is an average found by dividing the total population by the country’s total area. It is useful for comparing countries, but an average does not show where people actually live. A country may contain crowded cities and fertile valleys alongside deserts, mountains, forests, or other nearly empty regions.

When these very different areas are combined into one figure, the high and low densities are smoothed together. The national number may therefore look moderate even though some places are extremely crowded and others are sparsely settled. Option C correctly identifies this limitation. Option A is wrong because density applies to all areas, not only cities; B is wrong because total area is generally known; and D misunderstands the definition, which explicitly includes population.

Correct answer: A. Their populations and areas can differ while the ratio remains the same

Explanation: Population density is calculated as population divided by area, usually expressed as people per square kilometre. It is a ratio, so two countries can have different totals while producing the same result. For example, a country with 100,000 people and an area of 1,000 square kilometres has density 100 people per square kilometre. Another with 200,000 people and 2,000 square kilometres has the same density.

Thus, equal density does not require equal population or equal area. What must be equal is the relationship between the two quantities: population must increase in the same proportion as area. Therefore, option A is correct. Option B confuses a ratio with a total, while option C wrongly assumes that equal ratios require equal denominators. Option D is incorrect because the example shows that the situation is mathematically possible.

Correct answer: B. 50 percent

Explanation: To find how much larger A is than B, the increase must be compared with B, the original or reference value. The difference between the densities is \(240-160=80\) persons per square kilometre. The percentage increase is therefore \(\frac{80}{160}\times100=50\%\). This means A has half as much density again as B, or 50 percent more.

Option B is correct. Using 240 as the denominator would answer a different question, such as the difference as a percentage of A, and would give about 33.3 percent. Using only the numerical difference, 80, would not give a percentage. The phrase “higher than B” clearly makes B the base, so the supplied answer is mathematically consistent.

Correct answer: B. 25 percent

Explanation: The density increases from 180 to 225 persons per square kilometre. First find the absolute increase: 225 − 180 = 45 persons per square kilometre. To express this increase as a percentage, compare it with the original value, 180, rather than with the new value. Thus the required calculation is \(\frac{45}{180}\times100=25\%\). Option B is correct.

The number 45 is only the numerical increase, not the percentage increase. Dividing by 180 is essential because percentage change always uses the starting quantity as its base. The final density is therefore 125% of the original density, meaning it is 25% higher than the original. Hence 20%, 30%, and 45% do not follow from the given values.

Correct answer: C. 20 percent

Explanation: Percentage decrease compares the amount lost with the original amount, not with the final amount. The original density was 300 persons per square kilometre, and the new density is 240, so the loss is 60 persons per square kilometre. The correct base for the percentage is therefore 300, because that was the starting value.

Using the formula, percentage decrease = \(\frac{300-240}{300}\times100\) = \(\frac{60}{300}\times100\) = 20%. Thus option C is correct. The number 60 represents the absolute decrease, while 20% expresses that decrease relative to the original density. Dividing by 240 would answer a different question.

Correct answer: A. Area may remain unchanged

Explanation: Answer: A, the area may remain unchanged. Density is Population ÷ Area. Let the original population and area be P and A, so density is P/A. After the changes, population is 1.25P and density is 1.25P/A. For this ratio to have exactly that value, the area can remain A. In fact, if both population and density rise by the same factor, their ratio is unchanged only when area is unchanged. B would make the denominator larger and would prevent density from rising by the full 25%. C would make density rise by more than 25%, and D would also produce a different result. Since the wording says “may,” A is the valid conclusion.

Correct answer: C. Population will increase by 40 percent

Explanation: Answer: C, population will increase by 40 percent. Density equals population divided by area: D = P/A. If density must stay constant and area changes from A to 1.4A, the population must change from P to 1.4P so that the ratio remains the same: 1.4P ÷ 1.4A = P/A. Therefore population increases by 40 percent. A would make the ratio much smaller, because the numerator would fall while the denominator rises. B would also lower density because the same population would be spread over a larger area. D means a 100% increase and is more than required. Memory cue: constant density means population and area must change in the same proportion.

Correct answer: B. Density will increase by about 22.2 percent

Explanation: Density is the ratio of population to area. If the original population is P and area is A, the original density is \(P/A\). A 10 percent population increase changes the population to \(1.1P\), while a 10 percent area decrease changes the area to \(0.9A\). Both changes affect the ratio, so the percentages cannot simply be added without calculation.

The new density is \(\frac{1.1P}{0.9A}=\frac{1.1}{0.9}\frac{P}{A}=1.222\ldots\frac{P}{A}\). Thus it is about 22.2 percent higher. Option B is correct. A 20 percent increase is only a rough, incorrect addition of the two percentage changes.

Correct answer: A. It will decrease by about 18.2 percent

Explanation: Density is the ratio of population to area, so both changes must be included. Let the original population be \(P\) and area be \(A\). After a 10 percent population decrease, the population becomes \(0.9P\). After a 10 percent area increase, the area becomes \(1.1A\). The new density is therefore \(0.9P\div1.1A=0.81818(P\div A)\). It is about 81.8 percent of the original, so the decrease is about 18.2 percent. Option A is correct.

A simple subtraction of 10 percent and 10 percent would give 20 percent, but that is not the correct ratio calculation because the denominator also changes. The actual fall is \(1-0.81818=0.18182\), or approximately 18.2 percent. Since the question asks for an approximate change, the rounded value in option A is appropriate.

Correct answer: B. No because a small area can also produce high density

Explanation: High density means that many people live in relation to the amount of land. It does not by itself tell us that the region has a very large total population. A small area can have a high ratio even when its total number of residents is moderate. Total population and density are related, but they are not identical measurements.

Option B is correct because a compact city or small district may contain many people per square kilometre without containing more people than a much larger, less dense region. Option A incorrectly treats the two ideas as always equal. Options C and D misunderstand the fact that density depends on both population and area.

Correct answer: C. It can be high

Explanation: Population density depends on two quantities: population and area. A country may have few people in absolute terms but still have high density if its area is extremely small. For example, a population of 100000 spread over 100 square kilometres gives \(100000\div100=1000\) persons per square kilometre. This is a high density even though the total population may be small compared with that of a large country. Therefore, option C, “it can be high,” is correct.

The words “can be” are important. The density is not necessarily high in every such case; it depends on how small the area is relative to the population. It is not necessarily zero or low, and it can be calculated whenever both population and area are known. Thus, total population alone cannot determine density. The population-to-area ratio supports option C.

Correct answer: A. When population is very unevenly distributed within the region

Explanation: Arithmetic density is calculated as total population divided by total land area. It gives only one average for the whole region and does not show where people actually live. If most people are concentrated in a few cities while large areas are sparsely settled or empty, the average can hide this important contrast.

Therefore, option A is correct. Knowing population and area is necessary for calculation but does not make the measure misleading by itself. A small region or a whole-number result also does not create the problem. The issue is uneven spatial distribution within the region.

Correct answer: B. Average density is hiding internal spatial variation

Explanation: National density is an average for the entire country. In a mountainous country, large highland areas may be difficult to inhabit and may contain few people, while narrow valleys may provide water, transport routes, fertile land, and better living conditions. As a result, people can be strongly concentrated in valleys even though the countrywide average remains low. The correct choice is B.

The national figure combines population from crowded valleys with the large area of sparsely populated mountains. This averaging hides important internal spatial differences. A low national density therefore does not mean that every locality is sparse, and it does not show the exact density of the valleys. Option C is also wrong because valleys are part of the country and contribute to its population and density. A local map is needed to understand the contrast properly.

Correct answer: D. 800 persons per square kilometre

Explanation: Density is a ratio of population to area. When population remains constant but the area becomes smaller, the same number of people is concentrated in less land. Therefore the number of people per square kilometre rises. If the area is reduced to half, the density becomes twice as large, because dividing by one-half multiplies the quotient by two.

Starting with density 400, the new density is \(400 \div 0.5 = 800\), or equivalently \(400 \times 2 = 800\) persons per square kilometre. Hence option D is correct. A value of 200 would occur if the area doubled rather than halved, while 400 would require no change in area. The population being unchanged does not keep density unchanged when the denominator changes.

Correct answer: A. 250 persons per square kilometre

Explanation: Answer: A, 250 persons per square kilometre. Density is population divided by area. When area remains unchanged, density changes in exactly the same proportion as population. If the population becomes half, the density also becomes half: New density = 500 ÷ 2 = 250 persons per square kilometre. B is not half of 500. C would be correct only if population remained unchanged, but it becomes half. D is double the original value and would require the population to double at fixed area. The important condition is “area remains unchanged”; without that condition, population alone would not determine the new density.

Correct answer: B. Density will remain the same

Explanation: Density is a ratio: population divided by area. If both parts of a ratio are multiplied by the same non-zero number, the ratio does not change. This means that making a region three times larger while also making its population three times larger keeps the number of people per square kilometre unchanged.

Let the original population be \(P\) and area be \(A\). Original density is \(P/A\). After the change, it is \(3P/3A\). The factor 3 cancels, giving \(P/A\), exactly the original density. Therefore, option B is correct. It would triple only if population increased while area stayed unchanged.

Correct answer: B. 2 times

Explanation: Density changes according to the ratio of the change in population to the change in area. If the original population is P and area is A, the original density is \(P/A\). The new population is 3P and the new area is 1.5A. Thus the new density is \(3P/(1.5A)=2P/A\), so it is twice the original density. Option B is correct.

The population has tripled, which alone would make density three times larger. However, the area has also increased by one and a half times, reducing that effect. Dividing the population multiplier by the area multiplier gives \(3/1.5=2\). Therefore the answer is not three times or 4.5 times; the relevant operation is division because density equals population divided by area.

Correct answer: B. 150 persons per square kilometre

Explanation: A change in population changes density when the area stays fixed. First find the remaining population by subtracting the people who leave. Then divide that new population by the unchanged area. It is important not to subtract the number leaving directly from the density, because density is a ratio and must be recalculated using population and area.

The remaining population is 240000 − 60000 = 180000. The new density is therefore 180000 ÷ 1200 = 150 persons per square kilometre. Thus, option B is correct. The original density was 240000 ÷ 1200 = 200, and the fall to 150 makes sense because the population decreased while the area did not change. Option 200 is the old, not the new, density.

Correct answer: C. 240 persons per square kilometre

Explanation: When people migrate into a region, they are added to its existing population. If the area does not change, the new density is found by adding the migrants first and then dividing by the unchanged area. Migration changes population directly, whereas the stated land area remains fixed. The result is an average density for the whole region.

The new population is \(150000+30000=180000\). The area is still 750 square kilometres, so \(\text{Density}=\frac{180000}{750}=240\) persons per square kilometre. Therefore option C is correct. The value 200 is the old density, calculated before migration. The options 220 and 260 do not follow from the given increase and unchanged area.

Correct answer: B. 160 persons per square kilometre

Explanation: Answer: B, 160 persons per square kilometre. Use the formula Density = Population ÷ Area. The new population is 200,000 and the new area is 1,250 square kilometres. Therefore, density = 200,000 ÷ 1,250 = 160 persons per square kilometre. A is too low; 125 × 1,250 would give only 156,250 people. C is the old density, calculated from 200,000 ÷ 1,000, so it does not use the new area. D is also too high. Because the population stays fixed while the area increases, the same people are spread over a larger area, so density must decrease. Always use the new area in the final calculation.

Correct answer: B. 500 persons per square kilometre

Explanation: Density equals population divided by area. First find the unchanged population from the original figures: \(600\times300=180000\) people. When the area becomes 360 square kilometres, the same 180,000 people are spread over a larger area. The new density is therefore \(180000\div360=500\) persons per square kilometre. The correct choice is B.

The density falls because population remains fixed while area increases from 300 to 360 square kilometres. It cannot remain 600, since that value belonged to the smaller original area. It is also not 400 or 720: direct division gives 500. The calculation illustrates that, with population unchanged, increasing area lowers density, while decreasing area would raise it.

Correct answer: A. Productive land and easier settlement in plains can support more population

Explanation: Arithmetic density is the total population divided by the total land area, expressed as \(D=P/A\). It does not mean that every part of the area has the same conditions. Fertile plains generally offer productive soil, water, flatter land, easier construction and better transport. These advantages can support more people. Hills may have steep slopes, thinner soils and more difficult access, so fewer people may live there.

Option A is correct because it explains why population can be concentrated in plains. Options B and D are factually meaningless, while option C is wrong because arithmetic density uses population and area, not altitude.

Correct answer: B. Population is growing faster relative to area

Explanation: Population density measures how many people live in a unit of area. Its basic relationship is \(\text{Density}=\frac{\text{Population}}{\text{Area}}\). In an industrial corridor, factories and employment can attract many workers and families. If the physical or administrative area remains nearly unchanged while the number of residents rises, the number of people per square kilometre rises directly.

Option B states this numerical relationship correctly: population is increasing faster relative to area. Option A would generally reduce density if population did not rise enough, because a larger area spreads people out. Rainfall may influence settlement indirectly, but it is not the direct numerical reason for a rapid density increase. Therefore, B is correct.