Interest on capital is calculated as: \[ \text{Interest on Capital} = \text{Capital Amount} \times \text{Rate of Interest}. \] Assume Vivek's capital is ₹3,80,000, and the rate of interest is 15% per annum: \[ \text{Interest on Capital} = ₹3,80,000 \times 15% = ₹57,000. \] Thus, the correct answer is (C).
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 \(P,O,Q\).