Workings:
% Option
(A) Period of Operation: The firm started on 1st October 2023, and the year ends 31st March 2024. Thus, the operating period is 6 months.
% Option
(B) Interest on Capital (for 6 months):
\begin{itemize}
% Option
(C) Aakash: \( 80,00,000 \times 10 \times \frac{6}{12} = Rs 4,00,000 \)
% Option
(D) Baadal: \( 60,00,000 \times 10 \times \frac{6}{12} = Rs 3,00,000 \)
% Option
(E) Total Interest = Rs 4,00,000 + Rs 3,00,000 = Rs 7,00,000
\end{itemize}
% Option
(F) Divisible Profit: Profit before interest = Rs 13,00,000.
Divisible Profit = Rs 13,00,000 - Rs 7,00,000 (Total Interest) = Rs 6,00,000.
% Option
(G) Profit Distribution (Equal Ratio):
\begin{itemize}
% Option
(H) Aakash's Share = Rs 6,00,000 \(\times \frac{1}{2} = Rs 3,00,000 \)
% Option
(I) Baadal's Share = Rs 6,00,000 \(\times \frac{1}{2} = Rs 3,00,000 \)
\end{itemize}
% Option
(J) Baadal's Guaranteed Profit: Baadal's guaranteed profit after interest is Rs 7,00,000 per annum. For 6 months, the guarantee is Rs \( 7,00,000 \times \frac{6}{12} = Rs 3,50,000 \).
% Option
(K) Deficiency: Baadal's share = Rs 3,00,000, and his guaranteed profit = Rs 3,50,000. Hence, Deficiency = Rs 3,50,000 - Rs 3,00,000 = Rs 50,000.
% Option
(L) Meeting the Deficiency: Aakash meets the deficiency.
\begin{itemize}
% Option
(M) Aakash's Final Share = Rs 3,00,000 - Rs 50,000 = Rs 2,50,000
% Option
(N) Baadal's Final Share = Rs 3,00,000 + Rs 50,000 = Rs 3,50,000
\end{itemize}
Profit and Loss Appropriation Account for the year ended 31st March, 2024:
\[
\textit{(for the period 1st October 2023 to 31st March 2024)}
\]