A debtor can pay 87 paise in the rupee, but if his creditors would take $20\%$ of his debts, he could pay them and have ₹ 42 left. His debts and assets respectively are:

### Concept & Strategy This question relies heavily on understanding financial phrasing common in older aptitude tests. "Paying $87$ paise in the rupee" means the person's total assets amount to exactly $87\%$ of their total debts. "Taking $20\%$ off his debts" (implied by context, though phrased as "take $20\%$ of his debts" in the source) means the creditors accept an $80\%$ settlement. Formulating a simple algebraic equation linking assets, settled debts, and remainder solves the problem. ### Step-by-Step Solution * **Given:** Paying capacity = $87$ paise per rupee ($87\%$). Creditors accept a $20\%$ haircut (they settle for $80\%$ of the original debt). Amount left after settling = ₹ $42$. * **Calculation / Deduction:** Let the total debt be $D$. The debtor's assets ($A$) are $87\%$ of his debt. $A = 0.87D$ If the creditors accept $80\%$ of the debt (a $20\%$ reduction), the new amount payable is $0.80D$. The problem states that if he pays this new amount, he will have ₹ $42$ left over from his assets. Therefore, Assets - Settled Debt = Remainder $0.87D - 0.80D = 42$ $0.07D = 42$ Solving for $D$: $D = \frac{42}{0.07} = \frac{4200}{7} = 600$. So, his total debts are ₹ $600$. Now find his assets ($A$): $A = 0.87 \times 600 = 87 \times 6 = 522$. His assets are ₹ $522$. ### Exam Strategy & Shortcut Use option elimination based on the first condition: "Assets are $87\%$ of debts". Look at the options for (Debt, Asset): (a) $400, 520 \rightarrow \text{Asset} > \text{Debt}$ (Incorrect, he would be solvent) (b) $500, 521 \rightarrow \text{Asset} > \text{Debt}$ (Incorrect) (c) $600, 522 \rightarrow 0.87 \times 600 = 522$. (Perfect Match!) You don't even need to test the second condition. Understanding the initial ratio allows you to solve this in 5 seconds just by scanning the options. ### Common Pitfall The phrase "if his creditors would take 20% of his debts" is notoriously confusing. A modern reader might interpret this as creditors accepting exactly $20\%$, meaning the payable amount is $0.20D$. However, in classical financial aptitude contexts, "taking $20\%$" meant taking $20\%$ *off* (a discount), making the payable amount $80\%$. Always let the options guide ambiguous phrasing. ### Final Answer **Therefore, the correct answer is ₹ 600, ₹ 522.**