From the following information, prepare a Comparative Statement of Profit and Loss for the year ended $31^{\text {st }}$ March, 2024 :
| Particulars | 2023-24 (₹) | 2022-23 (₹) |
| Revenue from operations | 8,00,000 | 4,00,000 |
| Cost of revenue from operations | 4,00,000 | 2,00,000 |
| Employee benefit expenses | 1,60,000 | 80,000 |
| Tax Rate | 50% |
(a) From the following information, calculate Opening Trade Receivables and Closing Trade Receivables :
Let's calculate the Opening and Closing Trade Receivables.
1. Calculate Revenue from Operations (Credit Revenue):
Gross Profit Ratio = 20%
Cost of Revenue from Operations = Rs 6,40,000
Revenue from Operations = Cost of Revenue from Operations / (1 - Gross Profit Ratio)
Revenue from Operations = Rs 6,40,000 / 0.80 = Rs 8,00,000
Cash Revenue = (1/3) * Credit Revenue
Total Revenue from Operations = Cash Revenue + Credit Revenue
Rs 8,00,000 = (4/3) * Credit Revenue
Credit Revenue = Rs 8,00,000 * (3/4) = Rs 6,00,000
2. Calculate Average Trade Receivables:
Trade Receivables Turnover Ratio = Credit Revenue / Average Trade Receivables
4 = Rs 6,00,000 / Average Trade Receivables
Average Trade Receivables = Rs 6,00,000 / 4 = Rs 1,50,000
3. Let's denote Opening Trade Receivables as X:
Closing Trade Receivables = X + Rs 20,000
Average Trade Receivables = (Opening + Closing Trade Receivables) / 2
Rs 1,50,000 = (2X + Rs 20,000) / 2
Rs 3,00,000 = 2X + Rs 20,000
2X = Rs 2,80,000
X = Rs 1,40,000
4. Calculate Opening and Closing Trade Receivables:
Opening Trade Receivables = Rs 1,40,000
Closing Trade Receivables = Rs 1,40,000 + Rs 20,000 = Rs 1,60,000
Answer:
Opening Trade Receivables: Rs 1,40,000
Closing Trade Receivables: Rs 1,60,000
Simar, Tanvi and Umara were partners in a firm sharing profits and losses in the ratio of 5:6:9. On 31st March, 2024 their Balance Sheet was as follows:

Umara died on 30th June, 2024. The partnership deed provided for the following on the death of a partner:
From the following information, prepare a Comparative Income Statement of Arun Ltd. for the year ended 31st March, 2024. 
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 \(P,O,Q\).