To calculate goodwill using the super profit method, follow these
steps: 1. Calculate the capital employed: \[ {Capital Employed} = {Assets} - {Liabilities} = rupee 18,00,000 - rupee 3,00,000 = rupee 15,00,000 \]
2. Calculate the normal profit: \[ {Normal Profit} = {Capital Employed} \times {Normal Rate of Profit} \] \[ {Normal Profit} = rupee 15,00,000 \times \frac{10}{100} = rupee 1,50,000 \]
3. Calculate the super profit: \[ {Super Profit} = {Average Profit} - {Normal Profit} \] \[ {Super Profit} = rupee 2,00,000 - rupee 1,50,000 = rupee 50,000 \]
4. Calculate the goodwill: \[ {Goodwill} = {Super Profit} \times {Number of Years of Purchase} \] \[ {Goodwill} = rupee 50,000 \times 3 = rupee 1,50,000 \]
Final Answer Goodwill of the firm is rupee 1,50,000.

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 \(P,O,Q\).