Saloni and Mohini were partners in a firm sharing profits and losses in the ratio of 3 : 2. On 31st March, 2024, Saloni’s capital was 1,50,000. During the year, she withdrew 10,000 and introduced additional capital of 32,000. For the year ended 31st March, 2024, the firm earned a profit of 50,000. Saloni’s capital as on 1st April, 2023, was:

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 \(P,O,Q\).