The fixed capitals of Ridhima and Kavita are rupee 1,50,000 and rupee 2,00,000 respectively.
The partnership deed allows interest on capital at 8\% p.a. \[ \text{Interest on capital for Ridhima} = rupee 1,50,000 \times \frac{8}{100} = rupee 12,000 \] \[ \text{Interest on capital for Kavita} = rupee 2,00,000 \times \frac{8}{100} = rupee 16,000 \]
However, the net profit of the firm is rupee 21,000, which is insufficient to fully pay the interest on capital (rupee 28,000).
Hence, the available profit is distributed in the ratio of interest entitlements: \[ \text{Ratio of interest entitlement} = rupee 12,000 : rupee 16,000 = 3 : 4 \] \[ \text{Adjusted interest for Ridhima} = rupee 21,000 \times \frac{3}{7} = rupee 9,000 \] \[ \text{Adjusted interest for Kavita} = rupee 21,000 \times \frac{4}{7} = rupee 12,000 \]

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 \(P,O,Q\).