Step 1: Calculate Average Profit for Last 4 Years
₹ (3,00,000 + 4,00,000 + 5,00,000 + 4,00,000) ÷ 4 = ₹ 4,00,000
Step 2: Calculate Normal Profit
Capital Employed = ₹ 12,00,000
Normal Rate of Return = 10%
Normal Profit = 10% of ₹ 12,00,000 = ₹ 1,20,000
Step 3: Calculate Super Profit
Super Profit = Average Profit – Normal Profit = ₹ 4,00,000 – ₹ 1,20,000 = ₹ 2,80,000
Step 4: Calculate Goodwill
Goodwill = 3 × Super Profit = 3 × ₹ 2,80,000 = ₹ 8,40,000
Note: Partner salaries are already included in profit figures, so no further deduction is needed.
Balance Sheet of Chandan, Deepak and Elvish as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Fixed Assets | 27,00,000 | |
| Chandan | 7,00,000 | Stock | 3,00,000 |
| Deepak | 5,00,000 | Debtors | 2,00,000 |
| Elvish | 3,00,000 | Cash | 1,00,000 |
| General Reserve | 4,50,000 | ||
| Creditors | 13,50,000 | ||
| Total | 33,00,000 | Total | 33,00,000 |
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 \(P,O,Q\).