Madhu, Raj, Atul, and Prachi were partners in a firm sharing profit and losses in the ratio of 3:2:4:1. With effect from 1st April, 2023, they decided to share profits and losses equally. Their Balance Sheet showed a General Reserve of ₹1,00,000. The goodwill of the firm was valued at ₹20,00,000. Pass necessary journal entries for the above on account of change in the profit-sharing ratio. Show your working clearly.
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 \(P,O,Q\).