An increase in the ratio 5:6 means the population is multiplied by 6/5 from 2018 to 2020. A further increase in the ratio 6:7 multiplies it by 7/6 from 2020 to 2022. The combined effect from 2018 to 2022 is (6/5) × (7/6) = 7/5. Therefore, the 2022 population is 1,80,000 × (7/5) = 1,80,000 × 7 ÷ 5 = 2,52,000. Thus 2,52,000 is the correct population in 2022.
Option A:
Option A, 2,16,000, corresponds to multiplying by 6/5 only once and ignoring the second stage of growth. That would be the population if the increase stopped in 2020, not in 2022. Since the problem explicitly describes two successive increases, this option underestimates the final population.
Option B:
Option B, 2,40,000, might arise from an approximate or partial application of the ratios but does not correspond to the exact product 7/5. If we back-calculate, 2,40,000 × (5/7) ≈ 1,71,428.57, which does not match the original population of 1,80,000. Hence 2,40,000 is inconsistent with the data.
Option C:
Option C, 2,70,000, would require a combined multiplier of 2,70,000 ÷ 1,80,000 = 3/2. However, the actual combined multiplier from 5:6 and 6:7 is 7/5 = 1.4, not 1.5. Therefore this option overstates the population growth and cannot be correct.
Option D:
Option D is correct because it uses the proper composition of the two growth ratios, first 6/5 and then 7/6, yielding a neat combined factor of 7/5. The arithmetic leads precisely to 2,52,000, and reversing the process returns the original 1,80,000, demonstrating full consistency.
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