$A$ and $B$ have incomes in the ratio $5 : 3$. The expenses of $A$, $B$ and $C$ are in the ratio of $8 : 5 : 2$. If $C$ spends ₹ 2000 and $B$ saves ₹ 700, then $A$'s savings are

### Concept & Financial Ratios The fundamental financial equation is $\text{Income} = \text{Expense} + \text{Savings}$. By isolating known values in one ratio, you can solve for the multiplier and find all other related values. ### Step-by-Step Solution 1. **Given:** Expense ratio of $A : B : C$ is $8 : 5 : 2$. 2. Let their expenses be $8y$, $5y$, and $2y$ respectively. 3. We know $C$ spends ₹ 2000. So, $2y = 2000 \implies y = 1000$. 4. Calculate $B$'s expense: $5y = 5(1000) = 5000$. 5. Calculate $A$'s expense: $8y = 8(1000) = 8000$. 6. $B$ saves ₹ 700. Therefore, $B$'s Income = $B$'s Expense + $B$'s Savings = $5000 + 700 = 5700$. 7. **Given:** Income ratio of $A : B$ is $5 : 3$. Let their incomes be $5x$ and $3x$. 8. We know $B$'s income is 5700. So, $3x = 5700 \implies x = 1900$. 9. Calculate $A$'s income: $5x = 5(1900) = 9500$. 10. Finally, $A$'s savings = $A$'s Income - $A$'s Expense = $9500 - 8000 = 1500$. ### Exam Strategy & Shortcut Work backwards from the concrete numbers. $C$'s expense is 2000 (2 parts), so 1 expense part is 1000. $B$'s expense is 5000. $B$'s income is $5000 + 700 = 5700$. $B$ represents 3 income parts, so 1 income part is 1900. $A$'s income is $5 \times 1900 = 9500$. $A$'s expense is $8 \times 1000 = 8000$. $9500 - 8000 = 1500$. This can be done almost entirely mentally. ### Common Pitfall Using the same variable for both the income and expense ratios, which incorrectly assumes the scaling factor for income and expenses is identical. ### Final Answer Therefore, the correct answer is **₹ 1500**.