Jim and Joy were partners in a firm sharing profits and losses equally. On 1st April, 2024, they admitted John as a new partner for \(\frac{1}{5}\) share in the profits of the firm. On the date of John’s admission, the Balance Sheet of Jim and Joy showed a debit balance of 45,000 in the Profit and Loss Account.
From the following, what will be the accounting treatment for this balance on John’s admission?
Any accumulated losses (like debit balance in P&L A/c) should be borne by old partners in the old ratio before the admission of a new partner.

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 \(P,O,Q\).