Sudha and Sudhir were partners in a firm sharing profits and losses in the ratio of 4 : 1. On 1st April, 2023, their fixed capitals were ₹12,00,000 and ₹4,00,000 respectively. On 1st July, 2023, Sudha invested ₹2,00,000 as additional capital. On 1st August, 2023, Sudhir withdrew ₹50,000 from his capital.
The partnership deed provided for the following:
(i) Interest on capital @ 6% p.a.
(ii) Interest on drawings @ 8% p.a.
During the year, Sudha withdrew ₹60,000 and Sudhir withdrew ₹40,000 for personal use. After providing interest on capital and charging interest on drawings, the net profit of the firm for the year ended 31st March, 2024 was ₹3,50,000.
Prepare Current Accounts of Sudha and Sudhir.
| Dr. | Cr. | ||
|---|---|---|---|
| Particulars | ₹ | Particulars | ₹ |
| Drawings | 60,000 | Interest on Capital | 82,000 |
| Interest on Drawings | 2,400 | Profit transferred to Capital A/c | 2,80,000 |
| Total | 3,62,000 | ||
| Balance c/d | 2,99,600 | ||
| Total | 3,62,000 |
| Dr. | Cr. | ||
|---|---|---|---|
| Particulars | ₹ | Particulars | ₹ |
| Drawings | 40,000 | Interest on Capital | 22,500 |
| Interest on Drawings | 1,600 | Profit transferred to Capital A/c | 70,000 |
| Total | 92,500 | ||
| Balance c/d | 50,900 | ||
| Total | 92,500 |
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 \(P,O,Q\).