In a city, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. What percent of the total population comprises of females?

### Concept & Logic This problem requires a structured tree diagram or breakdown of a population based on percentages. The key is to start with a total base of $100$ and accurately divide it into nested subgroups (Migrants vs Locals, then Rural vs Urban) keeping track of percentages of percentages. ### Step-by-Step Solution * **Given:** Migrants = $35\%$ of total. Local = $65\%$ of total. Rural migrants = $20\%$ of migrants. Female demographics: $48\%$ of locals, $30\%$ of rural migrants, $40\%$ of urban migrants. * **Calculation / Deduction:** Assume the total population of the city is $100$. Number of migrants = $35$. Number of local population = $100 - 35 = 65$. Break down the migrants ($35$ total): Rural migrants = $20\%$ of $35 = 0.20 \times 35 = 7$. Urban migrants = $35 - 7 = 28$. Calculate the number of females in each respective category: Female locals = $48\%$ of $65 = 0.48 \times 65 = 31.2$. Female rural migrants = $30\%$ of $7 = 0.30 \times 7 = 2.1$. Female urban migrants = $40\%$ of $28 = 0.40 \times 28 = 11.2$. Total female population = $31.2 + 2.1 + 11.2 = 44.5$. Out of a base of $100$, this directly translates to $44.5\%$. ### Exam Strategy & Shortcut Map the data visually in a tree structure. Doing calculations sequentially directly reduces cognitive load. You can speed up the hardest arithmetic ($0.48 \times 65$) by using a nearby anchor: $(0.50 \times 65) - (0.02 \times 65) = 32.5 - 1.3 = 31.2$. This mental math trick saves precious time compared to margin scratchpad multiplication. ### Common Pitfall Students often misread the clause "20% of whom are from rural areas" as $20\%$ of the *total* population, rather than $20\%$ of the *migrants*. Always pay close attention to relative pronouns to know which base value to apply the percentage to. ### Final Answer **Therefore, the correct answer is 44.5%.**