Step 1: Understanding the Concept:
The question describes a situation where a debtor owes multiple debts to a single creditor and makes a partial payment. The legal issue is how this payment should be applied or "appropriated" to the various debts. The Indian Contract Act, 1872, provides a clear set of rules for this scenario.
Step 2: Detailed Explanation:
The rules for the appropriation of payments are contained in a specific chapter of the Indian Contract Act. Let's analyze the relevant sections:
\begin{itemize}
\item Section 59 (Application of payment where debt to be discharged is indicated): The first rule gives the right to the debtor. If the debtor expressly states or implies which debt the payment is for, the creditor must apply it accordingly.
\item Section 60 (Application of payment where debt to be discharged is not indicated): If the debtor does not specify, the right to appropriate shifts to the creditor. The creditor can apply the payment to any lawful debt, including a time-barred debt.
\item Section 61 (Application of payment where neither party appropriates): If neither the debtor nor the creditor makes any appropriation, the law steps in. The payment shall be applied in discharge of the debts in order of time, whether they are time-barred or not. If debts are of equal standing, the payment shall be applied proportionately.
\end{itemize}
These three sections, 59, 60, and 61, comprehensively cover the rules of appropriation. The other sections listed in the options deal with different topics (e.g., free consent, performance of contract).
Step 3: Final Answer:
The sections of the Contract Act that provide the answer to the appropriation of payments are Section 59 to 61.