A sum of ₹ 1250 is divided among A, B, C so that A gets $\frac{2}{9}$ of B's share and C gets $\frac{3}{4}$ of A's share. The share of C is

### Concept & Chained Proportions When individual shares are expressed as fractions of another person's share, it is often simplest to express all shares in terms of a single person's share before equating their sum to the total amount. $$ \text{Total} = A + B + C $$ ### Step-by-Step Solution 1. **Define the relationships:** We are given: $A = \frac{2}{9}B \implies B = \frac{9}{2}A$ $C = \frac{3}{4}A$ 2. **Express the total sum in terms of A:** The total sum is ₹ 1250. $A + B + C = 1250$ Substitute B and C in terms of A: $A + \frac{9}{2}A + \frac{3}{4}A = 1250$ 3. **Solve for A:** Find a common denominator, which is 4: $\frac{4A}{4} + \frac{18A}{4} + \frac{3A}{4} = 1250$ $\frac{25A}{4} = 1250$ $25A = 5000 \implies A = 200$ 4. **Calculate C's share:** $C = \frac{3}{4}A = \frac{3}{4} \times 200 = 150$ ### Exam Strategy & Shortcut You can also assign a ratio. $A:B = 2:9$ and $C:A = 3:4 \implies A:C = 4:3$. Combine ratios: Make A the same in both. Multiply $A:B$ by 2 $\implies A:B = 4:18$. Now, $A:B:C = 4:18:3$. Total parts = $4 + 18 + 3 = 25$. Multiplier = $1250 \div 25 = 50$. C's share = $3 \times 50 = 150$. This avoids fractions entirely! ### Common Pitfall A common mistake is trying to solve for B first, which leads to messy fraction multiplication. Picking the variable that connects both (in this case, A) makes the math much cleaner. ### Final Answer Therefore, the correct answer is **₹ 150**.