Bittu and Chintu were partners in a firm sharing profit and losses in the ratio of 4 : 3. Their Balance Sheet as at 31st March, 2024 was as follows:
On 1st April, 2024, Diya was admitted in the firm for \( \frac{1}{7} \)th share in the profits on the following terms:
Prepare Revaluation Account and Partners' Capital Accounts.
1. Revaluation Account
| Particulars | Amount (₹) | Particulars | Amount (₹) |
|---|---|---|---|
| Fixed Assets (Overvaluation) | 1,40,000 | Creditors (Settlement) | 70,000 |
| Profit on Revaluation: | |||
| Bittu (4/7) | 40,000 | ||
| Chintu (3/7) | 30,000 | ||
| Total | 1,40,000 | Total | 1,40,000 |
Explanation:
2. Partners' Capital Accounts
| Particulars | Bittu (₹) | Chintu (₹) | Diya (₹) | Particulars | Bittu (₹) | Chintu (₹) | Diya (₹) |
|---|---|---|---|---|---|---|---|
| To Revaluation A/c | 40,000 | 30,000 | By Balance b/d | 8,00,000 | 6,00,000 | ||
| To General Reserve A/c (4/7) | 1,20,000 | 90,000 | By General Reserve A/c (₹ 2,10,000*4/7) | 1,20,000 | 1,20,000 | ||
| By Bank (Capital) | 5,60,000 | ||||||
| To Bank A/c | By Bank(Goodwill) | 5,60,000 | |||||
| By Partner capital/ premium | 5,60,000 | ||||||
| To Balance c/d | 15,20,000 | 6,60,000 | 5,60,000 | ||||
| Total | 16,80,000 | 7,80,000 | 5,60,000 | Total | 16,80,000 | 7,80,000 | 5,60,000 |
Explanation:
Working Notes for Diya Capital Calculation:
Given that, Diya was admitted for 1/7th share
Thus, the capital bought by Diya must be
-1/7th * of total capital=560000
-7* 560000= 560000, the amount paid by Diya will be paid as goodwill to the partners
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 \(P,O,Q\).