Bittu and Chintu were partners in a firm sharing profits and losses in the ratio of 4 : 3. Their Balance Sheet as at 31st March, 2024 was as follows:
| Liabilities | Amount (₹) | Assets | Amount (₹) |
| Capitals: | Fixed Assets | 15,40,000 | |
| Bittu | 8,00,000 | Stock | 3,50,000 |
| Chintu | 6,00,000 | Debtors | 1,40,000 |
| General Reserve | 2,10,000 | Bank | 70,000 |
| Creditors | 4,90,000 | ||
| Total | 21,00,000 | Total | 21,00,000 |
On 1st April, 2024, Diya was admitted in the firm for 1⁄7 share in the profits on the following terms:
Prepare Revaluation Account and Partners’ Capital Accounts.
| Particulars | Amount (₹) | Particulars | Amount (₹) |
| To Fixed Assets (Decrease) | 1,40,000 | By Creditors (Saving) | 70,000 |
| By Loss transferred: | |||
| Bittu’s Capital A/c | 40,000 | ||
| Chintu’s Capital A/c | 30,000 | ||
| Total | 1,40,000 | Total | 1,40,000 |
Loss on Revaluation = ₹ 70,000 distributed in 4 : 3 ratio
Bittu’s share = ₹ 70,000 × 4/7 = ₹ 40,000
Chintu’s share = ₹ 70,000 × 3/7 = ₹ 30,000
Adjustment for General Reserve:
Bittu’s share = ₹ 2,10,000 × 4/7 = ₹ 1,20,000
Chintu’s share = ₹ 2,10,000 × 3/7 = ₹ 90,000
Adjustment for goodwill premium brought by Diya:
Diya brings ₹ 5,60,000
Divided in sacrificing ratio = old ratio – new ratio
Old ratio = 4 : 3
New ratio = 3 : 3 : 1
Sacrifice of Bittu = 4/7 – 3/7 = 1/7
Sacrifice of Chintu = 3/7 – 3/7 = 0
Thus entire premium goes to Bittu = ₹ 5,60,000
Capital of Diya = 1/7 of firm’s total capital = 1/7 × ₹ 21,00,000 = ₹ 3,00,000
Total brought in by Diya = ₹ 3,00,000 + ₹ 5,60,000 = ₹ 8,60,000
Revaluation loss ₹ 70,000 distributed and goodwill adjusted. Diya’s capital and premium recorded.
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 \(P,O,Q\).