The expenses of $A$ and $B$ are in the ratio $2 : 3$. A sum of ₹ 2800 is equally divided between them. If $A$ saves ₹ 600, then $B$ saves

### Concept & Income-Expense Identity The fundamental financial identity is: $\text{Income} - \text{Savings} = \text{Expenses}$. Use this relation individually for $A$ and $B$. ### Step-by-Step Solution 1. **Given:** Total sum = ₹ 2800 divided equally. So, Income of $A = 1400$ and Income of $B = 1400$. 2. $A$ saves ₹ 600. Therefore, Expenses of $A = \text{Income} - \text{Savings} = 1400 - 600 = 800$. 3. The ratio of expenses of $A$ and $B$ is $2 : 3$. Let their expenses be $2x$ and $3x$. 4. We know $A$'s expenses are $2x = 800 \implies x = 400$. 5. Therefore, $B$'s expenses are $3x = 3(400) = 1200$. 6. $B$'s savings = Income of $B - \text{Expenses of } B = 1400 - 1200 = 200$. ### Exam Strategy & Shortcut Realize that $A$'s expense (800) represents "2 parts" of the ratio. Thus, "1 part" is 400. $B$'s expense is "3 parts", meaning 1200. Since $B$ received 1400, savings are simply $1400 - 1200 = 200$. No complex algebra required. ### Common Pitfall Dividing the initial ₹ 2800 sum in the $2:3$ ratio, rather than interpreting it as equal incomes. ### Final Answer Therefore, the correct answer is **₹ 200**.