Raju, Sohan, and Tina are partners in a firm sharing profits and losses in the ratio of 2 : 2 : 1. Tina is guaranteed a minimum amount of ₹40,000 as a share of profit every year. Any deficiency arising on that account shall be borne by Raju. If profit of the firm for the year ended 31st March, 2023 is ₹1,60,000, Raju will bear a deficiency of:
Step 1: Calculate Tina's profit share. \[ \text{Tina's share of profit} = \frac{1}{5} \times 1,60,000 = ₹32,000. \] Step 2: Determine the deficiency. \[ \text{Deficiency} = ₹40,000 - ₹32,000 = ₹8,000. \] Since Raju is responsible for the deficiency, he will bear ₹8,000.
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 \(P,O,Q\).