A sum of money is divided among 160 males and some females in the ratio 16 : 21. Individually each male gets ₹ 4 and a female ₹ 3. The number of females is

### Concept & Ratio of Totals vs Individuals The total amount received by a group is the product of the number of individuals in that group and the amount each individual receives. $$\text{Total Amount for Group} = \text{Number of People} \times \text{Amount per Person}$$ ### Step-by-Step Solution 1. **Given:** - Number of males = 160 - Amount per male = ₹ 4 - Amount per female = ₹ 3 - Ratio of total male money to total female money = $16 : 21$ 2. **Calculate Total Male Amount:** Total money received by all males = $160 \times 4 = 640$. 3. **Use Ratio to Find Total Female Amount:** Let total male money be $16x$ and total female money be $21x$. $16x = 640 \implies x = 40$. Total money received by all females = $21x = 21 \times 40 = 840$. 4. **Calculate Number of Females:** Since each female gets ₹ 3, the number of females is: $$\text{Number of Females} = \frac{\text{Total Female Money}}{\text{Amount per Female}} = \frac{840}{3} = 280$$ ### Exam Strategy & Shortcut Set up a single proportion equation: $\frac{\text{Total Male Money}}{\text{Total Female Money}} = \frac{160 \times 4}{F \times 3} = \frac{16}{21}$. Solve for $F$: $\frac{640}{3F} = \frac{16}{21} \implies 16 \times 3F = 640 \times 21 \implies 48F = 13440 \implies F = 280$. ### Common Pitfall Confusing the ratio of total money with the ratio of individuals. Always differentiate between total pool ratios and per-head ratios. ### Final Answer Therefore, the correct answer is **280**.