Sanju and Manju were partners in a firm sharing profits and losses in the ratio of 3:2. Their Balance Sheet on 31st March, 2023 was as follows:
\[ \begin{array}{|l|r|l|r|} \hline \textbf{Liabilities} & \textbf{Amount (₹)} & \textbf{Assets} & \textbf{Amount (₹)} \\ \hline \text{Capitals:} & & \text{Plant and Machinery} & 80,000 \\ \quad \text{Sanju} & 1,40,000 & \text{Furniture} & 1,32,000 \\ \quad \text{Manju} & 1,20,000 & \text{Investments} & 60,000 \\ \quad \text{Total Capitals} & 2,60,000 & \text{Debtors} & 76,000 \\ \text{General Reserve} & 40,000 & \text{Less: Provision for doubtful debts} & (4,000) \\ \text{Creditors} & 1,80,000 & \text{Cash at Bank} & 1,36,000 \\ \hline \text{Total Liabilities} & 4,80,000 & \text{Total Assets} & 4,80,000 \\ \hline \end{array} \]
Adjustments:
- Furniture was to be depreciated by ₹6,000.
- Investments were valued at ₹72,000.
- Plant and Machinery was taken over by Sanju and Manju in their profit-sharing ratio.
- Uday will bring in proportionate capital and ₹10,000 as his share of goodwill premium in cash.
Revaluation Account: \[ \begin{array}{|l|r|l|r|} \hline \textbf{Dr.} & \textbf{Amount (₹)} & \textbf{Cr.} & \textbf{Amount (₹)} \\ \hline \text{Furniture (Depreciation)} & 6,000 & \text{Investments (Appreciation)} & 12,000 \\ \hline \text{Profit transferred to:} & & & \\ \quad \text{Sanju’s Capital A/c} & 3,600 & & \\ \quad \text{Manju’s Capital A/c} & 2,400 & & \\ \hline \text{Total} & 12,000 & \text{Total} & 12,000 \\ \hline \end{array} \]
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 \(P,O,Q\).