We calculate Keshav's opening capital using the formula: \[ \text{Opening Capital} = \text{Closing Capital} - \text{Net Profit} + \text{Drawings} - \text{Interest on Drawings} \]
Given: - Closing Capital = rupee 55,000 - Keshav’s Share of Profit = \( \frac{3}{5} \times rupee 15,000 = rupee 9,000 \)
- Drawings during the year = rupee 1,500 × 4 = rupee 6,000
- Interest on Drawings: \[ \text{Interest} = rupee 6,000 \times 8\% \times \frac{6.5}{12} = rupee 260 \]
Now, applying the formula: \[ \text{Opening Capital} = rupee 55,000 - rupee 9,000 + rupee 6,000 - rupee 260 \] \[ = rupee 52,000 \]
Thus, the correct answer is rupee52,000 (Option D).

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 \(P,O,Q\).