Sudarshan’s capital = ₹ 3,60,000 × 1/4 = ₹ 90,000
Remaining capital = ₹ 3,60,000 – ₹ 90,000 = ₹ 2,70,000
Divide ₹ 2,70,000 in ratio 9 : 5 : 4:
- Aman = (9/18) × ₹ 2,70,000 = ₹ 1,35,000
- Govind = (5/18) × ₹ 2,70,000 = ₹ 75,000
- Guru = (4/18) × ₹ 2,70,000 = ₹ 60,000
Adjustments:
- Aman brought in ₹ 75,000 more (already had ₹ 60,000)
- Govind withdrew ₹ 5,000 (already had ₹ 80,000)
- Guru brought in ₹ 15,000 more (already had ₹ 45,000)
Journal Entries:
| Particulars | Dr. (₹) | Cr. (₹) |
|---|---|---|
| Bank A/c To Sudarshan’s Capital A/c (Capital brought by Sudarshan) | 90,000 | 90,000 |
| Bank A/c To Aman’s Capital A/c To Guru’s Capital A/c (Cash brought in for capital adjustments) | 90,000 | 75,000 15,000 |
| Govind’s Capital A/c To Bank A/c (Excess capital withdrawn by Govind) | 5,000 | 5,000 |
Balance Sheet of Atharv and Anmol as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Fixed Assets | 14,00,000 | |
| Atharv | 8,00,000 | Stock | 4,90,000 |
| Anmol | 4,00,000 | Debtors | 5,60,000 |
| General Reserve | 3,50,000 | Cash | 10,000 |
| Creditors | 9,10,000 | ||
| Total | 24,60,000 | Total | 24,60,000 |
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Sundry Creditors | 1,80,000 | Cash in hand | 30,000 |
| General Reserve | 20,000 | Debtors | 1,20,000 |
| Capitals: | Kishore – 6,00,000 | Stock | 1,50,000 |
| Ranjan – 4,00,000 | Furniture | 1,00,000 | |
| Land and Building | 8,00,000 | ||
| Total | 12,00,000 | Total | 12,00,000 |
Aryan and Adya were partners in a firm sharing profits and losses in the ratio of 3 : 1. Their Balance Sheet on 31st March, 2024 was as follows :
Balance Sheet (Before Dev's Admission)
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capital: Aryan | 3,20,000 | Machinery | 3,90,000 |
| Capital: Adya | 2,40,000 | Furniture | 80,000 |
| Workmen’s Compensation Reserve | 20,000 | Debtors | 90,000 |
| Bank Loan | 60,000 | Less: Provision for Doubtful Debts | (1,000) |
| Creditors | 48,000 | Net Debtors | 89,000 |
| Stock | 77,000 | ||
| Cash | 32,000 | ||
| Profit and Loss A/c | 20,000 | ||
| Total | ₹6,88,000 | Total | ₹6,88,000 |
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 \(P,O,Q\).