Mita and Vihaan were partners in a firm sharing profits and losses in the ratio of 3:2.
On 31st March, 2024 their Balance Sheet was as follows:
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Sundry Creditors | 2,00,000 | Cash | 50,000 |
| Capitals: | Sundry Debtors | 2,00,000 | |
| Mita | 4,00,000 | Less: Provision for Doubtful Debts | (7,000) |
| Vihaan | 3,00,000 | 1,93,000 | |
| Stock | 2,50,000 | ||
| Plant and Machinery | 3,50,000 | ||
| Patents | 57,000 | ||
| Total | 9,00,000 | Total | 9,00,000 |
On the above date, Zen was admitted as a new partner for 4/15 share in the profits on the following terms:
Pass necessary journal entries for the above transactions in the books of the firm on Zen’s admission
(i) Capital and Goodwill Premium:
Zen brings ₹3,00,000 as capital and goodwill share:
Total goodwill = ₹4,12,500 ⇒ Zen’s share = 4/15 × ₹4,12,500 = ₹1,10,000
Sacrificing ratio: Mita : Vihaan = 3:2 (old) ⇒ Zen gets from Mita only ⇒ Mita sacrifices 4/25, Vihaan 0.
Entire goodwill of ₹1,10,000 goes to Mita.
(ii) Revaluation of Assets and Liabilities:
New provision = 5% of ₹2,00,000 = ₹10,000 ⇒ Increase = ₹3,000
Stock decreased = ₹50,000
Plant & Machinery appreciated = ₹50,000
Patents appreciated = ₹63,000
Omitted liability = ₹30,000 (to be added)
Revaluation Profit = (Appreciation) - (Depreciation + Additional liability)
= ₹(50,000 + 63,000 + 50,000) - ₹(50,000 + 3,000 + 30,000) = ₹1,63,000 - ₹83,000 = ₹80,000
Profit shared in old ratio 3:2: Mita = ₹48,000, Vihaan = ₹32,000
| Particulars | Dr. (₹) | Cr. (₹) |
|---|---|---|
| Cash A/c Dr. To Zen’s Capital A/c To Mita’s Capital A/c (Goodwill) | 4,10,000 | 3,00,000 1,10,000 |
| Provision for Doubtful Debts A/c Dr. Stock A/c Dr. To Revaluation A/c | 3,000 50,000 | 53,000 |
| Revaluation A/c Dr. To Plant and Machinery A/c To Patents A/c To Outstanding Liabilities A/c | 1,63,000 | 50,000 63,000 30,000 |
| Revaluation A/c Dr. To Mita’s Capital A/c To Vihaan’s Capital A/c | 80,000 | 48,000 32,000 |
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 \(P,O,Q\).