Population Growth

Correct answer: B, 8.55 million, or 85.5 lakh. First convert the percentage to a decimal: 5 percent equals 0.05. The decrease is 9,000,000 × 0.05 = 450,000. Subtract this decrease from the original population: 9,000,000 − 450,000 = 8,550,000, which is 8.55 million or 85.5 lakh. A is wrong because it subtracts too much, giving 8.25 million. C is wrong because it subtracts only 0.3 million, not 5 percent of 9 million. D is wrong because 9.45 million is obtained by adding 5 percent, so it represents a 5 percent increase rather than a decline. The safe method is: final population = original population × (1 − rate). Here, 9 × 0.95 = 8.55 million.

Correct answer: C, 50 years. The Rule of 70 gives an approximate doubling time by dividing 70 by the annual growth rate expressed as a percentage. Thus, doubling time = 70 ÷ 1.4 = 50 years. This rule is an estimate and assumes that the rate remains approximately constant. A, 35 years, would correspond to a higher growth rate of about 2 percent. B, 40 years, results from using an unsuitable divisor or rounding incorrectly. D, 70 years, would be the estimate for a growth rate of about 1 percent, not 1.4 percent. The idea is that faster growth produces a shorter doubling time, while slower growth produces a longer one. Memory cue: “70 divided by the percentage gives years to double.” Actual population doubling can differ if fertility, mortality, or migration changes.

Answer: A. Natural increase is calculated by subtracting the death rate from the birth rate. Initially, it is 14 − 6 = 8 per thousand. After the birth rate falls, it becomes 12 − 6 = 6 per thousand. The change is 6 − 8 = −2 per thousand, so the natural increase decreases by 2 per thousand. A is correct because the result is a fall of two units. B is wrong because 6 is the unchanged death rate, not the amount of change. C has the wrong direction: a lower birth rate with the same death rate cannot increase natural growth. D is wrong because the birth rate has changed and therefore the difference has changed. The safest method is to calculate the natural increase twice and compare the two results. Memory cue: if deaths stay constant, a fall in births reduces natural increase by exactly the same amount.

Answer: D. Total percentage growth is calculated from the absolute increase divided by the initial population, multiplied by 100. The increase is 12.1 − 10 = 2.1 million. Therefore, percentage growth is 2.1 ÷ 10 × 100 = 21%. D is correct. A, B, and C are incorrect because none equals the calculated 21%. The five-year period tells us how long the increase took, but the question asks for total growth, not the average annual rate or annual compound rate. It would be a mistake to divide 21% by five without being asked for an average, or to calculate a compound annual rate. Memory cue: total percentage change = (final − initial) ÷ initial × 100; the initial value is always the denominator.

Answer: B. First find the absolute change: 24 − 23.52 = 0.48 million, so the population has declined. Percentage change is calculated relative to the initial population: 0.48 ÷ 24 × 100 = 2%. Therefore, the population decreased by 2%. A is too small. C is wrong because the final population is lower than the initial population, so the change cannot be an increase. D confuses the numerical difference, 0.48 million, with a percentage; 4.8 is not the correct percentage relative to 24 million. The sign should be negative if written algebraically: −2%. Memory cue: percentage change uses the starting value as the base and the direction comes from whether the final value is higher or lower.

The correct answer is C: 40%. The increase is 42 million − 30 million = 12 million. Percentage growth is measured against the initial population: (12 ÷ 30) × 100 = 40%.

The correct answer is C: 25 percent. Begin by finding the absolute increase: 60 million − 48 million = 12 million. Next compare that increase with the initial population, not the final population. Percentage growth = (12 ÷ 48) × 100 = 25 percent. Thus, the population grew by one-fourth of its original size. Option A is incorrect because 20 percent of 48 million is 9.6 million, not the actual increase of 12 million. Option B is also too low. Option C is correct because 12 is one-quarter of 48, and one-quarter equals 25 percent. Option D is too high; 30 percent of 48 million would be 14.4 million. A common mistake is to divide the increase by 60 million, which would measure the increase against the final total rather than the original base. Memory cue: percentage growth always uses the starting population as the reference unless the question explicitly states another base.