Population Density

Answer: C. Overall city density is an average: total population divided by the entire city area. That entire area may include parks, forests, factories, roads, and other land where few or no residents live. If many people live in a smaller residential portion, the population is concentrated there, so some residential neighbourhoods can have a density much higher than the citywide average. A is not necessary; non-residential land can lower the overall average. B is not required because averages do not describe every part equally. D is too absolute; residential density can be calculated if the residential population and residential area are known. Remember: an overall average can hide substantial local differences.

Arithmetic density is an average calculated by dividing total population by total area. An average does not show where people are located within that area. Two regions can have the same population-to-area ratio while their people are arranged very differently. One region may have homes and villages spread across much of the land, whereas another may have most residents in a few cities and very few people elsewhere.

Thus, option A is correct. Equal arithmetic density does not require equal settlement patterns, equal-sized cities, or evenly distributed residents. Option B incorrectly treats an average as a complete description. Option C is unnecessary because the regions need not have equal areas; their population and area ratios can still match. Option D is also too broad, because density provides useful average information even though it does not show detailed distribution.

Density tells us how many people live in one unit of area. To compare how many times B is as dense as A, divide B's density by A's density. This comparison is a ratio, not a subtraction. A ratio of 2 means that B has twice as many people per unit area as A, under the given density values.

Here, the required ratio is \(500 \div 250 = 2\). Therefore, Region B's density is 2 times, or double, Region A's density. The difference between the densities is 250, but that only tells us how much larger B's density is in absolute terms; it does not answer the “how many times” question. Thus, option B is correct.

A ratio compares two quantities by writing them in the same order and reducing them by a common factor. Here the order is A:B, so the required ratio is 360:240. Both numbers describe density in the same unit, persons per square kilometre, so they can be compared directly. The ratio does not require finding the difference or deciding how much larger A is than B.

Divide both terms by their greatest common factor, 120. Thus, 360 ÷ 120 = 3 and 240 ÷ 120 = 2, giving 3:2. Therefore, option B is correct. This means that for every 2 equal parts of density in Region B, Region A has 3 parts. The option 2:1 would incorrectly suggest that A has twice B's density, but 360 is only one and a half times 240.

Answer: C, 1,200 square kilometres. Start with Density = Population ÷ Area. Rearranging the formula gives Area = Population ÷ Density. Substitute the values: Area = 420,000 ÷ 350 = 1,200 square kilometres. A, B, and D do not give the stated population when multiplied by 350. For a check, 350 × 1,200 = 420,000, so the result is consistent. The units also support the answer: people divided by people per square kilometre leaves square kilometres. A useful method is to remember the triangle: Population is above Density and Area; therefore, Area = Population ÷ Density.

Answer: C, 250 persons per square kilometre. Population density is calculated by dividing population by area: Density = 275,000 ÷ 1,100. Cancel two zeros to obtain 2,750 ÷ 11, and 2,750 ÷ 11 = 250. Therefore, the density is 250 persons per square kilometre. A would give only 220,000 people when multiplied by 1,100. B would give 247,500 people, and D would give 302,500 people, so neither reproduces the stated population. The unit must be persons per square kilometre because people are divided by square kilometres. Check the answer by multiplying 250 × 1,100 = 275,000.

Population is obtained by multiplying the number of people per square kilometre by the number of square kilometres. The density is 125 persons per square kilometre, and the area is 1,600 square kilometres. Because every square kilometre has the same stated average density, multiplying these two values gives the region’s total population.

Calculate \(125\times1600\). First, \(125\times16=2000\), and then restore the two zeros from 1,600, giving 200,000. Therefore, option C is correct. The other values do not result from the correct density-area multiplication; in particular, 250,000 would require a density of 156.25 persons per square kilometre for this area.

With area unchanged, population and population density are directly proportional. Therefore, the percentage increase in population is the same as the percentage increase in density. Density rises from 80 to 100, so the absolute increase is 20 persons per square kilometre. The percentage increase is \(\frac{20}{80}\times100=25\%\). Hence the correct choice is B, 25 percent.

The original value, 80, must be used as the base when finding a percentage increase. Dividing the increase by the new value would not give the standard percentage increase. Since the area is fixed, no separate area adjustment is needed. The density has become 1.25 times its earlier value, which means population has also become 1.25 times its earlier value, or increased by 25 percent.

With population unchanged, density and area move in opposite directions because \(Density = Population \div Area\). If density falls while population stays constant, the area must increase. Let the original population be \(P\). The original area is \(P\div200\), and the new area is \(P\div160\). Thus the new area divided by the old area is \(200\div160=1.25\).

A ratio of 1.25 means that the new area is 125% of the original area. The increase is therefore 25%, not 20%, because the percentage must be calculated relative to the original area. Hence option C, area increased by 25%, is correct. The 20% figure describes the fall in density, not the corresponding increase in area.

Density is a relative measure: it compares the number of people with the amount of area they occupy. Therefore, saying that a city has density above the national average means that the city has more people per unit of area than the countrywide average. This conclusion concerns concentration, not necessarily the total number of people. A small city may be very dense, while a large country may have a much greater total population.

Option A states exactly what the comparison means and is therefore correct. Option B confuses density with total population; the city need not contain more people than the whole country. Option C is also unsupported because density does not mean that the city is larger than the national area. Option D is wrong because a national average can validly be higher or lower than a city's density.

Arithmetic density is calculated by dividing total population by total land area, usually expressed as persons per square kilometre. It is useful for comparing broad areas, but it is only an average. It does not show whether people are concentrated in cities, river valleys, or coastal belts while other parts remain nearly empty.

Consequently, option B states its major limitation correctly: an average value can hide internal concentration and variation. Option A is false because both population and area are required. Option C is false because arithmetic density can be calculated for any area, not only rural places. Option D is false because persons per unit area is its normal expression.

The correct answer is A. A density comparison is reliable only when the values use the same measurement unit and refer to areas defined in comparable ways. For example, persons per square kilometre can be directly compared with persons per square kilometre when both regions are measured using similar boundary rules. If necessary, units such as hectares and square kilometres must first be converted to a common unit.

Without this consistency, an apparent difference may be caused by measurement rather than by a real difference in population concentration. Option B compares incompatible units without conversion. C introduces boundary definitions that may not represent equivalent areas, and D compares a total population with a density, which are different quantities. Thus common units and comparable boundaries are essential for a fair direct comparison.

Population density is not simply the number of people in a place. It is the relationship between population and the area occupied. The basic formula is (\(Density = \frac{Population}{Area}\)\u0000). Medium-level questions may also change population, area, boundaries, or migration, so the effect of each change must be considered proportionally rather than guessed from one number.

Therefore, option B is correct. If population rises while area stays constant, density rises; if area expands while population stays constant, density falls. If both change, their relative percentage changes must be compared. Option A ignores area, C wrongly treats every large population as dense, and D removes the essential variable from the calculation.

Population density tells us how many people live in one square kilometre. To find the total population, we multiply the number of people per square kilometre by the total area. The units also show why multiplication is needed: persons per square kilometre multiplied by square kilometres leaves persons. Therefore, the suitable answer is option B, 90,000 people.

Using the formula \(\text{Total population}=\text{density}\times\text{area}\), substitute the given values: \(180\times500=90,000\). Thus, a region covering 500 square kilometres at a density of 180 persons per square kilometre contains 90,000 people. Option A is too small, while options C and D are greater than the calculated value.

Arithmetic population density is calculated as total population divided by total area. To find area, rearrange the relationship as \(\text{Area}=\frac{\text{Population}}{\text{Density}}\). The population is 150,000 and the density is 250 persons per square kilometre. Dividing gives \(150000\div250=600\) square kilometres.

Therefore, option B is correct. The units also confirm the result: persons divided by persons per square kilometre leaves square kilometres. Choosing 500 would correspond to a density of 300 persons per square kilometre, while 750 and 1000 do not satisfy the given ratio. The calculation uses total population and total area, not only inhabited land.

Population density equals population divided by area. If the area remains unchanged, any percentage change in population produces the same percentage change in density. This is because the denominator of the ratio is fixed, so the ratio rises or falls exactly with the numerator. The relationship is direct and proportional for this situation.

Suppose the original population is P and the fixed area is A. The original density is \(P/A\). After a 20 percent increase, the population is \(1.2P\), so the new density is \(1.2P/A=1.2(P/A)\). Thus density also increases by 20 percent, making option A correct. It does not increase by only 10 percent, decrease, or remain constant.

Population density means the number of people living in a unit of area. If the number of people does not change but the area becomes larger, those same people are spread over more space. Consequently, fewer people are found in each square kilometre, so density decreases rather than increases or remaining constant.

Let the original population be P and the original area be A. The initial density is \(P/A\). After a 25 percent increase, the new area is \(1.25A\), while the population is still P. The new density is therefore \(P/(1.25A)\), which is 0.8 times the original density. Thus it falls by 20 percent, making option B correct. It does not double.

Density equals population divided by area. The two regions have the same population, but A covers only 400 square kilometres while B covers 800 square kilometres. Thus the same number of people is concentrated in half the area in A. For equal populations, the smaller area always produces the greater density. If the common population is represented by \(P\), then A has density \(P/400\), while B has \(P/800\); the first value is twice the second.

Option A is correct. Region B has more land for the same population, so its people are more widely spread and its density is lower. The exact population is unnecessary for this comparison. Options C and D overlook the different areas, while option B reverses the effect of area. Therefore A has the higher population density.

Density is population divided by area: \(Density=\frac{Population}{Area}\). Since regions X and Y have the same area, the denominator in both calculations is identical. In that situation, the region with the larger population automatically has the larger density. X has 90,000 people, whereas Y has 120,000, so Y has 30,000 more people distributed over the same amount of land.

Therefore, option B, region Y, is correct. We do not need the actual common area to compare the densities; if it were \(A\), the densities would be \(90000/A\) and \(120000/A\), and the second value would be larger. Option C would be true only if the populations were also equal, while option D incorrectly overlooks the equal-area information.

Because the area remains unchanged, the percentage change in population is exactly the percentage change in population density. The fall is \(180000-144000=36000\). Relative to the original population, this is \(36000/180000\times100=20\%\). The new population is also 80% of the original, so density becomes 80% of its former value and falls by 20%.

Option C is correct. A 10% or 15% decrease uses the wrong fraction, while 25% would not match the actual reduction. The unchanged area is important: if area had also changed, density would need to be recalculated using both the new population and new area. Here only the numerator changes, so the density percentage decrease is the same as the population percentage decrease.

Population density tells us how many people live in one square kilometre. To find the total population, multiply the density by the total area. This works because every square kilometre contains the stated average number of people, so adding the people across all square kilometres gives the population of the whole city.

Here, the density is 600 persons per square kilometre and the area is 250 square kilometres. Thus, \(600\times250=150000\). The unit “per square kilometre” cancels with square kilometres, leaving people. Therefore, the city has 150,000 people, so option B is correct. Options with 120,000, 180,000, or 240,000 result from using an incorrect multiplication.

Density is defined as population divided by area. Therefore, when population and density are known, area is found by dividing the total population by the population density. The units also show this clearly: people divided by people per square kilometre leaves square kilometres.

The calculation is \(360000\div450=800\). Equivalently, 450 multiplied by 800 gives 360,000, confirming the result. Hence the district covers 800 square kilometres, so option C is correct. The other choices do not produce the stated population when multiplied by 450. It is important not to multiply population and density, because that would not represent an area.

Population density measures how many people occupy a given unit of area, such as one square kilometre. A high value means people are concentrated relative to land area, but it does not reveal the total number of people in the whole country or region. Total population depends on both density and the size of the area. In simplified form, total population equals density multiplied by area.

Therefore, option B is correct. A small country may have a very high density but a smaller total population than a large country with lower density. Option A is wrong because high density does not always mean the largest population. C reverses the idea: a large area alone does not create high density. D is also wrong because density and total population are mathematically related, even though one does not determine the other alone.

Average population density is calculated as \(D=\frac{P}{A}\). If two countries have equal density, their population-to-area ratios are equal: \(\frac{P_1}{A_1}=\frac{P_2}{A_2}\). Suppose the first country has three times the population of the second, so \(P_1=3P_2\). Substituting this into the equality shows that its area must also be three times as large.

Thus option A is correct: the more populous country will have about three times the area, assuming the densities are exactly equal. The conclusion follows from the density formula, not from population size alone. “About” allows for rounded population or density figures. Options B and C reverse or ignore the required proportional relationship, while D is incorrect because equal density directly links population and area.

Density gives the number of people in each square kilometre. If the density and the area are known, the total population is found by multiplying them. The square-kilometre unit in the density matches the square-kilometre unit of the area, so the area part is counted the required number of times and the result is people.

The calculation is \(250 \times 1200 = 300000\). Therefore the population is 300,000 people, which is option B. The other choices come from using an incorrect multiplier or from making an arithmetic error. A reverse check also works: \(300000 \div 1200 = 250\) people per square kilometre, exactly the given density.