
| Particulars | Amount (₹) | Particulars | Amount (₹) |
|---|---|---|---|
| To Furniture A/c (1,20,000 − 1,00,000) | 20,000 | By Plant & Machinery A/c (4,35,000 − 4,05,000) | 30,000 |
| To Profit on Revaluation transferred to: | By Creditors A/c | 5,000 | |
| Asha’s Capital A/c (3/5) = 9,000 Indra’s Capital A/c (2/5) = 6,000 | |||
| Total | 35,000 | Total | 35,000 |
| Dr. | Cr. | ||||||
|---|---|---|---|---|---|---|---|
| Particulars | Asha (₹) | Indra (₹) | Suraj (₹) | Particulars | Asha (₹) | Indra (₹) | Suraj (₹) |
| To Furniture A/c | 1,00,000 | - | - | By Balance b/d | 4,00,000 | 3,00,000 | - |
| By General Reserve A/c | 30,000 | 20,000 | - | ||||
| By Revaluation A/c (Profit) | 9,000 | 6,000 | - | ||||
| By Premium for Goodwill A/c | 15,000 | 10,000 | - | ||||
| By Bank A/c (Capital) | - | - | 2,30,000 | ||||
| To Balance c/d | 3,54,000 | 3,36,000 | 2,30,000 | ||||
| Total | 4,54,000 | 3,36,000 | 2,30,000 | Total | 4,54,000 | 3,36,000 | 2,30,000 |
Old Ratio (Asha : Indra) = \( 3 : 2 \) Suraj’s Share = \( \frac{1}{4} \) Remaining Share = \[ 1 - \frac{1}{4} = \frac{3}{4} \] Asha’s New Share: \[ \frac{3}{4} \times \frac{3}{5} = \frac{9}{20} \] Indra’s New Share: \[ \frac{3}{4} \times \frac{2}{5} = \frac{6}{20} \] Suraj’s Share: \[ \frac{1}{4} = \frac{5}{20} \] New Ratio = **9 : 6 : 5** ---
Firm’s Goodwill = ₹ 1,00,000 Suraj’s Share of Goodwill: \[ 1,00,000 \times \frac{1}{4} = 25,000 \] ---
Asha’s Sacrifice: \[ \frac{3}{5} - \frac{9}{20} = \frac{12}{20} - \frac{9}{20} = \frac{3}{20} \] Indra’s Sacrifice: \[ \frac{2}{5} - \frac{6}{20} = \frac{8}{20} - \frac{6}{20} = \frac{2}{20} \] Sacrificing Ratio = **3 : 2** ---
Asha’s Share: \[ 25,000 \times \frac{3}{5} = 15,000 \] Indra’s Share: \[ 25,000 \times \frac{2}{5} = 10,000 \] ---
Increase in Plant & Machinery = ₹ 30,000 Decrease in Furniture = ₹ 20,000 Creditors no longer payable = ₹ 5,000 Net Profit: \[ 30,000 + 5,000 - 20,000 = 15,000 \] Distributed: - Asha = ₹ 9,000 - Indra = ₹ 6,000 ---
Total Capital of Old Partners: \[ 3,54,000 + 3,36,000 = 6,90,000 \] This represents \( \frac{3}{4} \) of total capital. \[ \text{Total Firm Capital} = 6,90,000 \times \frac{4}{3} = 9,20,000 \] Suraj’s Capital: \[ 9,20,000 \times \frac{1}{4} = 2,30,000 \] Total brought by Suraj: \[ 2,30,000 + 25,000 = 2,55,000 \]

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 \(P,O,Q\).