Population Growth

When a population grows by the same percentage every year, each new increase is calculated on the population reached in the previous year. This is compound growth, not simple addition. The starting population is 4 million and the annual growth factor is 1.06, so after three years the value is calculated as \(4\times1.06^3\) million.

Since \(1.06^3=1.191016\), the final population is about 4.764064 million, or 47.64 lakh. Therefore, option B is the closest and correct answer. Simply adding 6 percent three times would give 18 percent and about 4.72 million, but that ignores the fact that the second and third increases apply to an already enlarged population.

Successive percentage changes must be applied one after another to the changing amount; they should not simply be added or subtracted. Take the initial population as 100. A 50 percent increase changes it to 150. The later 30 percent decline is calculated on 150, not on the original 100. Thirty percent of 150 is 45, so the final population is \(150-45=105\).

The final value 105 is 5 more than the initial value 100, which is a 5 percent increase. Therefore, option A is correct. Equivalently, the combined multiplier is \(1.5\times0.7=1.05\). A direct subtraction of 30 from 50 would give 20 percent, but that would incorrectly use the same base for both changes.

Natural increase is found by subtracting the death rate from the birth rate. Initially, it was \(38-14=24\) per thousand. After the change, it becomes \(29-11=18\) per thousand. Thus, natural increase falls by 6 per thousand. Both rates have declined, but the birth rate has fallen by 9 per thousand while the death rate has fallen by only 3 per thousand, so the difference becomes smaller. Migration is not included in this calculation.

Choice A is correct: natural increase changes from 24 to 18 per thousand. Choice B would be correct only if the new death rate were 8 rather than 11, so it does not match the given figures. Choice C adds the two rates instead of finding their difference, and choice D merely repeats the old and new death rates. The calculation concerns births minus deaths, not either rate separately.

A large reproductive-age population can create demographic momentum because many people are in the ages when they may have children. However, this effect depends on how many of those people remain in the country and form families there. If long-term out-migration from this group accelerates, the number of potential parents inside the country may fall. Thus option A is the best answer: future births and demographic momentum may weaken.

The word “may” is important. Out-migrants could later return, and fertility patterns may differ between migrants and those who stay, so the exact effect cannot be guaranteed. Nevertheless, fewer reproductive-age adults generally means fewer births occurring within the country, all else being equal. Option B is too absolute, option C ignores the changed population composition, and option D does not follow because migration does not automatically reduce mortality.

Natural change includes births minus deaths, while net migration records arrivals minus departures. Here natural change is -15,000 and net migration is +15,000, so the two effects cancel and the total population change is zero. Even so, the people being lost and gained may have different ages, occupations, and skills. Therefore option A is possible: age structure and labour-market composition can change.

For instance, if most deaths are among older residents and most incoming migrants are young working adults, the city may become relatively younger and have a larger working-age share, even though its total size is unchanged. The calculation only describes the net total; it does not say that every age group remains constant. Births and deaths do not become zero, and neither the land area nor all demographic characteristics must stay unchanged.

A natural increase rate measures the difference between births and deaths, without including migration. A rate of 14 per thousand means that, on average, there are 14 more people for every group of 1,000 people during one year. Since migration is zero, the natural increase is also the total population change caused by births minus deaths in that year.

The population is 45 million, or 45,000,000 people. Applying the rate gives \(45{,}000{,}000 \times \frac{14}{1000} = 630{,}000\). Thus, the natural increase is 630,000 people in one year, so option C is correct. The answer is not 14 percent; “per thousand” must be converted by dividing by 1,000. Zero migration does not make the increase zero because births still exceed deaths.

A natural increase rate measures the change caused only by births and deaths; it does not include migration. A rate of \(-2.25\) per thousand means that, on average, the population loses 2.25 people for every 1,000 people in one year. The negative sign shows a natural decrease rather than a natural increase.

The calculation is \(80{,}000{,}000 \times \frac{-2.25}{1000} = -180{,}000\). The minus sign indicates a loss, so the natural change is a decrease of 180,000 people. Migration could alter the total population change, but it is not part of this calculation. Therefore, option C is correct; the other numerical choices do not result from applying the given rate to 80 million.

Total population growth combines natural growth with net migration. Natural growth may be positive or negative, so its sign must be retained during calculation. Here natural growth is \(-0.9\) percent and net migration is \(+1.5\) percent.

Adding the signed rates gives \(-0.9+1.5=+0.6\) percent. Thus, migration more than compensates for the natural decrease, and the total population rises by 0.6 percent. Option C is therefore correct. Option D incorrectly adds the two absolute magnitudes, while option A treats the migration gain as if it were also negative. Option B results from subtracting in the wrong direction.

Total population growth is the sum of natural increase and net migration. Rearranging this relationship gives net migration as total growth minus natural increase. Percentages must be kept with their signs: positive natural increase adds people, while negative net migration removes people.

The calculation is \(-0.7-0.8=-1.5\) percent. Therefore, net migration is -1.5 percent, so option A is correct. The negative sign indicates net out-migration. Although natural increase added 0.8 percent, an outflow of 1.5 percent was larger, leaving total growth at -0.7 percent.

A fall in births immediately makes only the newest infant group smaller. It does not remove children who were born in earlier years. Those larger groups continue to grow older and enter the usual secondary-school age range. Therefore, school demand responds with a time lag rather than changing in the same year. The correct choice is A because earlier-born cohorts are still moving toward secondary education. Choice C is wrong: fewer births do not make the teenage population instantly zero.

Population planning must consider the age structure already present, not only the latest birth figures. Even if births fall sharply today, many children already alive will need schools several years later. Demand may decline gradually when the smaller cohorts reach secondary-school age. Thus, the existing population momentum explains why education facilities cannot be reduced immediately, and why planners use cohort projections when estimating future schools.

Age groups are made up of cohorts, meaning people born during roughly the same period. A large number of births several decades ago can create a large cohort that later moves into the 40-to-59 age group. If births are currently low, the 0-to-9 group will be smaller. These two observations can therefore occur together: an older large cohort is moving through middle age while fewer children are being born now. Age structure records the effects of past birth patterns over time.

Choice A is correct because it explains both trends at once. A large earlier cohort raises the size of the middle-aged population, while low current fertility reduces the child population. Choice B is too absolute; age groups do not always change in the same direction. Choice C is wrong because a fall in births affects younger groups first and does not immediately remove people already in middle age. Choice D ignores the important link between birth history and age structure.

Zero net migration describes only the numerical balance between arrivals and departures. It does not mean that the two groups have the same ages, education, occupations, or skills. If more high-skilled young adults arrive while lower-skilled older adults leave, the total population may remain unchanged but its composition can improve. Hence option A is correct: human capital and the working-age structure may improve.

For example, equal numbers entering and leaving produce net migration of zero, but the incoming group may add workers, qualifications, and productive capacity, while the departing group removes fewer working-age people and more older dependants. This can alter the labour supply and average skill level without doubling the population. The change in natural increase is not fixed by this information, so option D is too strong. Option C wrongly assumes that a zero total balance means no demographic effect.

The Rule of 70 estimates the annual percentage growth rate from doubling time. Its approximate relationship is \(r \approx 70/T\), where \(r\) is the annual growth rate in percent and \(T\) is the doubling time in years. This is a shortcut rather than an exact population projection, but it is suitable for the stated estimate.

With a doubling time of 32 years, \(r \approx 70\div32=2.1875\) percent per year. Rounding this value to two decimal places gives approximately 2.19 percent. Thus option C is correct. The value 2 percent is a rougher rounding, while 2.5 percent would correspond to a shorter doubling time. The estimate also assumes that the growth rate is reasonably stable during the period considered.

The Rule of 70 is a quick way to estimate how long a population or investment takes to double when its annual growth rate stays fairly constant. The important point is that the rate must be used as a percentage, not as a decimal fraction. A smaller growth rate leads to a longer doubling time, because growth is happening more slowly.

Here the annual growth rate is 0.4 percent. Apply the rule: doubling time = 70 ÷ 0.4 = 175 years. Therefore, the estimated doubling time is 175 years, which matches option D. The other values do not result from dividing 70 by 0.4; for example, using 70 years would incorrectly treat the rate as 1 percent.

Growth in two successive years is compounded because the second percentage applies to the population after the first year’s increase. If the initial population is represented by 100, after a 14 percent rise it becomes 114. A further 6 percent rise is calculated on 114, not on the original 100.

The combined multiplier is \(1.14\times1.06=1.2084\). Thus the final population is 120.84 percent of the starting population, giving a total increase of 20.84 percent. Option B is therefore correct. Adding 14 percent and 6 percent gives only 20 percent and misses the additional 0.84 percent produced when the second increase acts on the first year’s increase.

Successive percentage changes must be applied one after another to the changed amount. They cannot be combined by simply subtracting 25 from 35, because the second percentage is calculated from the population after the first change. A convenient starting value is 100, which represents 100 percent of the original population.

After a 35 percent increase, 100 becomes 135. A 25 percent decrease removes \(25\%\) of 135, which is \(135\times0.25=33.75\). The final value is \(135-33.75=101.25\). Compared with the original 100, this is a 1.25 percent increase. Thus, option A is correct.

Age structure describes how many people belong to different age groups. An ageing country has a relatively large elderly population and often a smaller working-age share. Young migrants, especially when they arrive over many years, add people mainly to the working-age group. They can also later contribute to births, although that is not necessary for the immediate effect.

Option A is the most likely result. The number and share of working-age people may increase, while the elderly share of the total population may become smaller or grow more slowly for some time. This does not permanently end ageing, because migrants also grow older and future fertility and mortality matter. The elderly population cannot immediately fall to zero, and migration clearly changes age structure. Therefore A is correct.

Total population is made up of several age groups, so it can rise even when one group becomes smaller. An ageing population may contain more elderly people, while the working-age group may shrink because adults migrate out or because fewer young people are entering it. The important idea is that total growth does not require every age group to grow.

Option A is correct because it combines these two possible demographic changes: a rising elderly population and a declining working-age population. A large older cohort can increase total numbers through longer survival, while emigration or smaller birth cohorts reduce the working-age supply. Options B and C contradict the stated decline, and D would not explain population growth. The exact contribution of migration and births would require data, but A is the most plausible explanation.

Child mortality and fertility affect the size of younger age groups in different but connected ways. When child mortality falls, a larger proportion of children survive. If fertility remains high at the same time, many new births continue to enter the population. Together, these conditions can produce a large young cohort and strengthen demographic momentum. Therefore option A is the best answer.

A large cohort will eventually move into the reproductive ages. Even if fertility later begins to decline, the large number of potential parents can keep births relatively high for some time. This is why the effect may continue beyond the ten-year period mentioned. The result is not that young people immediately disappear, nor that future births become zero. Option D is also incorrect because survival and fertility changes directly affect age structure.

The key idea is to compare the growth of the whole population with the growth of children aged 0–14. The city grew by 35%, but its child population grew by only 1%. This means that children account for very little of the increase. The strongest reasonable interpretation is that many people in other age groups, especially young adults or working-age people, moved into the city. Such migration may be connected with jobs, education, housing, or services. The figures do not prove the exact cause, but they make this explanation more plausible than the alternatives.

Option A follows because in-migration of other age groups can raise total population without producing a similar rise in the child group. Option B is too certain: the data do not show that the birth rate rose by 35%. Option C contradicts the given 1% growth of children, and option D is unjustified because the two figures can occur together. Therefore, A is the strongest conclusion.

Net migration is calculated as in-migration minus out-migration. It shows the balance, not the total number of movements. If 100,000 people enter and 99,000 leave, net migration is only 1,000, but almost 200,000 movements have occurred. Such large flows can change the population’s age, skills, occupations, or cultural composition, especially if arrivals and departures have different characteristics. A near-zero net value therefore does not mean that migration is unimportant.

Choice A is correct because high gross flows can coexist with almost zero net migration and can still alter population composition. Choice B is the opposite of the evidence: large arrivals and departures mean that mobility is high. Choice C incorrectly treats the number of arrivals as small, and choice D denies the stated out-migration. The key distinction is between net migration, which measures balance, and total mobility, which measures the scale of movement.

A percentage rate is applied to the population base. The country has 300 million people, and the annual total growth rate is 0.27 percent. Convert the percentage to a decimal by dividing by 100, then multiply it by the population.

The calculation is \(300000000\times\frac{0.27}{100}=810000\). Therefore, the simple increase in one year is 810,000 people, so option C is correct. This is an increase in number of people, not a new population total. Options A, B, and D result from using an incorrect percentage or multiplying by the wrong rate. Even a small rate can produce a large absolute increase when the population base is very large.

To find a percentage decrease, first calculate how much the population fell and then compare that decrease with the original population. The original population was 75 million, and the later population was 71.25 million. Therefore, the decrease is \(75-71.25=3.75\) million. The original value, not the final value, is used as the base.

The percentage decrease is \((3.75/75)\times100=5\) percent. Equivalently, 71.25 million is 95 percent of 75 million, so the loss is 5 percent. Therefore option C is correct. Option B would result from using an incorrect base or calculation, while 3 percent and 7.5 percent do not match the actual change.

Zero net migration means that the number arriving equals the number leaving. It does not mean that the two groups have the same ages or that migration has no demographic effect. The age composition of migrants matters even when the numerical balance is zero. Replacing older residents with younger arrivals changes the population structure.

Here, arrivals have an average age of 23 and departures have an average age of 68. A younger group replaces an older group, so the average age may fall and the working-age share may rise. This information alone cannot show that the total population will double, that natural increase is zero, or that age structure will remain unchanged. Thus option A follows from the age difference.

A falling birth rate usually reduces the proportion of children and gradually raises the median age. However, the total population does not have to decline immediately. A large number of people born in an earlier period may still enter childbearing or working ages, creating demographic momentum. Lower mortality and positive net migration can also continue to add people. The combined pattern is therefore an ageing population that is still growing, but more slowly than before. Complete stability would require no net increase, which is not stated.

The clues point in the same direction: falling births mean slower natural increase and fewer young cohorts, while a rising median age shows ageing. Continued population growth means that past age structure, survival, or migration is still strong enough to offset the decline in births for the present. Thus, the situation is not rapid rejuvenation or high fertility. Option A accurately combines ageing with continuing but slower growth.