Population composition with adult gender ratio: In a town, 80% of the population are adults. Among adults, men and women are in the ratio 9 : 7. If the number of adult women is 4.2 lakh, find the total population of the town.

Introduction / Context:
Population structure problems commonly require moving between subgroup counts and overall totals using ratios and percentages. Here we move from adult women to adult total, and then to the overall population using the adult percentage.

Given Data / Assumptions:

• Adults = 80% of total population.
• Adult men : adult women = 9 : 7.
• Adult women = 4.2 lakh.

Concept / Approach:
If adult women represent the “7 parts” in the 9 : 7 ratio, total adults correspond to 9 + 7 = 16 parts. Compute adult total from women, then scale up from 80% to get the town’s population.

Step-by-Step Solution:
Adult total = (16/7) * 4.2 lakh = 9.6 lakh.Adults are 80% of total ⇒ Total population = Adult total / 0.8.Total = 9.6 / 0.8 = 12 lakh.

Verification / Alternative check:
Adults = 12 × 0.8 = 9.6 lakh; women share = 7/16 of 9.6 = 4.2 lakh, consistent with the given data.

Why Other Options Are Wrong:

• 9.6 lakh is adult total, not overall population.
• 9.8 and 11.6 lakh do not match the ratio-percentage chain.

Common Pitfalls:

• Using 7/9 instead of 7/16 for the women fraction of adult total.
• Forgetting to scale adults to overall total using 80%.

Final Answer:
12 lakh