Ratan, Singh and Sharma were partners in a firm sharing profits and losses in the ratio of 2 : 2 : 1. Their Balance Sheet on 31st March, 2024 was as follows:Balance Sheet of Ratan, Singh and Sharma as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Creditors | 90,000 | Bank | 65,000 |
| Outstanding Wages | 10,000 | Stock | 1,50,000 |
| General Reserve | 3,00,000 | Debtors | 90,000 |
| Less: Provision for Doubtful Debts | (5,000) | ||
| 85,000 | |||
| Capital A/cs: | Plant and Machinery | 2,50,000 | |
| Ratan | 3,60,000 | Land and Building | 4,50,000 |
| Singh | 2,40,000 | Profit and Loss A/c | 1,00,000 |
| Sharma | 1,00,000 | ||
| Total | 11,00,000 | Total | 11,00,000 |
On 1st April, 2024 Sharma retired from the firm on the following terms :
(i) Plant and Machinery is revalued at ₹2,00,000.
(ii) Land and Building was to be appreciated by ₹49,500 and provision for bad debts will be maintained at 5% of the debtors.
(iii) Sharma's share in the goodwill of the firm was valued at ₹60,000 and the retiring partner's share was adjusted through the capital accounts of remaining partners.
(iv) Sharma was paid in cash brought by Ratan and Singh in such a way so as to make their capitals proportionate to their new profit sharing ratio.
Prepare Revaluation Account and Partners' Capitals Accounts.
| Particulars | Amount (₹) | Particulars | Amount (₹) |
|---|---|---|---|
| To Plant & Machinery A/c (Decrease in Value) | ₹50,000 | By Land & Building A/c (Appreciation) | ₹49,500 |
| To Provision for Doubtful Debts A/c (5% of ₹90,000) | ₹4,500 | By Loss transferred to Capital A/cs: | |
| Ratan’s Capital (2/5 of ₹5,000) | ₹2,000 | ||
| Singh’s Capital (2/5 of ₹5,000) | ₹2,000 | ||
| Sharma’s Capital (1/5 of ₹5,000) | ₹1,000 | ||
| Total | ₹54,500 | Total | ₹54,500 |
| Particulars | Ratan (₹) | Singh (₹) | Sharma (₹) |
|---|---|---|---|
| To Sharma’s Capital (Goodwill Adjustment) | ₹2,000 | ₹2,000 | ₹1,000 |
| To Bank A/c (Settlement) | ₹24,000 | ₹16,000 | – |
| By Balance b/d | ₹3,60,000 | ₹2,40,000 | ₹1,20,000 |
| By General Reserve | ₹1,20,000 | ₹40,000 | – |
| By Profit and Loss A/c | ₹40,000 | – | – |
| By Ratan’s Capital A/c (Goodwill) | – | ₹1,19,000 | – |
| By Singh’s Capital A/c (Goodwill) | – | ₹1,00,000 | – |
| By Sharma’s Capital A/c (Goodwill) | ₹60,000 | ₹20,000 | ₹24,000 |
| Total | ₹5,42,000 | ₹3,98,000 | ₹2,00,000 |
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 \(P,O,Q\).