(i) Settlement of Mansha’s loan with unrecorded furniture:
\[ \text{Mansha’s Loan A/c Dr.} \quad ₹18,000 \\ \text{Profit on settlement (Transferred to Realisation A/c) Dr.} \quad ₹2,000 \\ \text{To Realisation A/c (Unrecorded Furniture)} \quad ₹20,000 \] Explanation: Furniture was not recorded, so its value settled Mansha’s loan and extra ₹2,000 was a loss.
(ii) Sale of Machinery at 10% loss:
\[ \text{Bank A/c Dr.} \quad ₹72,000 \\ \text{Realisation A/c Dr.} \quad ₹8,000 \\ \text{To Machinery A/c / Realisation A/c} \quad ₹80,000 \] Explanation: Machinery sold at a 10% loss. Loss = ₹8,000, sale value = ₹72,000.
(iii) Creditor settled by cash and stock:
\[ \text{Realisation A/c Dr.} \quad ₹6,000 \\ \text{To Bank A/c} \quad ₹21,000 \\ \text{To Stock A/c} \quad ₹25,000 \\ \text{To Creditors A/c} \quad ₹40,000 \] Explanation: Total payment = ₹46,000, but liability = ₹40,000 ⇒ excess paid = ₹6,000 (loss).
(iv) Payment of Bank Loan with Interest:
\[ \text{Bank Loan A/c Dr.} \quad ₹1,00,000 \\ \text{Interest A/c Dr.} \quad ₹10,000 \\ \text{To Bank A/c} \quad ₹1,10,000 \] OR \[ \text{Realisation A/c Dr. ₹10,000} \\ \text{Bank Loan A/c Dr. ₹1,00,000} \\ \text{To Bank A/c ₹1,10,000} \] Explanation: Interest on loan at the time of dissolution is a Realisation expense.
(v) Sale of Investments with brokerage:
\[ \text{Bank A/c Dr.} \quad ₹63,000 \\ \text{To Realisation A/c} \quad ₹63,000 \\ \text{Realisation A/c Dr.} \quad ₹2,000 \\ \text{To Bank A/c} \quad ₹2,000 \] Explanation: Brokerage is an expense on sale, so it’s charged to Realisation A/c.
(vi) Profit and Loss A/c shown on Asset Side:
\[ \text{Partners’ Capital A/c Dr.} \quad ₹30,000 \\ \text{To Profit and Loss A/c} \quad ₹30,000 \] Explanation: Accumulated loss (fictitious asset) is distributed among partners’ capital accounts.
Balance Sheet of Madhavan, Chatterjee and Pillai as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Creditors | 1,10,000 | Cash at Bank | 4,05,000 |
| Outstanding Expenses | 17,000 | Stock | 2,20,000 |
| Mrs. Madhavan’s Loan | 2,00,000 | Debtors | 95,000 |
| Chatterjee’s Loan | 1,70,000 | Less: Provision for Doubtful Debts | (5,000) |
| Capitals: | Madhavan – 2,00,000 | Land and Building | 1,82,000 |
| Chatterjee – 1,00,000 | Plant and Machinery | 1,00,000 | |
| Pillai – 2,00,000 | |||
| Total | 9,97,000 | Total | 9,97,000 |
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Machinery | 7,00,000 | |
| Madhur | 9,00,000 | Investments | 4,00,000 |
| Neeraj | 8,00,000 | Debtors | 11,00,000 |
| Creditors | 6,00,000 | Stock | 2,00,000 |
| Bills Payable | 2,00,000 | Cash at Bank | 1,00,000 |
| Total | 25,00,000 | Total | 25,00,000 |
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).