Step 1: Capital balance on date of death = ₹3,00,000
Step 2: Interest on capital for 6 months (from 1st April to 1st October)
Interest = ₹3,00,000 × 10% × \( \frac{6}{12} \) = ₹15,000
Step 3: Share in General Reserve
Total reserve = ₹60,000
Chandni’s share = \( \frac{5}{10} \times 60,000 = ₹30,000 \)
Step 4: Share in Goodwill
Goodwill of firm = ₹1,20,000
Chandni’s share = \( \frac{5}{10} \times 1,20,000 = ₹60,000 \)
Step 5: Share in Profit till date of death (6 months)
Previous year’s profit = ₹4,50,000
Profit for 6 months = ₹4,50,000 × \( \frac{6}{12} \) = ₹2,25,000
Chandni’s share = \( \frac{5}{10} \times 2,25,000 = ₹1,12,500 \)
Step 6: Total Due to Chandni’s Executors:
| Particulars | Amount (₹) |
|---|---|
| Capital Balance | 3,00,000 |
| Add: Interest on Capital | 15,000 |
| Add: Share of General Reserve | 30,000 |
| Add: Share of Goodwill | 60,000 |
| Add: Share of Profit till death | 1,12,500 |
| Total Amount Payable | 5,17,500 |
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 \(P,O,Q\).