1. Annual Profit of the Firm = rupee 4,50,000
2. Sukriti’s Profit-Sharing Ratio = \( \frac{2}{5} \) \[ {Sukriti’s Annual Share of Profit} = 4,50,000 \times \frac{2}{5} = rupee 1,80,000 \]
3. Profit for the Period from 1superscript{st} April 2023 to 30superscript{th} June 2023 (3 months): Since the profit is for one full year, we calculate Sukriti’s share for 3 months (April–June): \[ {Sukriti’s Profit for 3 months} = 1,80,000 \times \frac{3}{12} \] \[ = 1,80,000 \times \frac{1}{4} = rupee 45,000 \]
Thus, the amount credited to Sukriti’s Capital Account = rupee45,000 (Option B).

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 \(P,O,Q\).