Prepare a Common Size Balance Sheet of ZXT Ltd. from the following information:
A Common Size Balance Sheet expresses every item as a percentage of the total balance sheet figure (i.e., total assets or total liabilities).
It helps in analysing the proportion of each item and comparing across years.
Here, the base (total) is:
- For 2023: ₹ 20,00,000
- For 2024: ₹ 50,00,000
We compute each item as:
Common Size % = (Item Value ÷ Total) × 100
Common Size Balance Sheet of ZXT Ltd.
(as at 31st March, 2024 and 31st March, 2023)
| Particulars | 31.03.2024 (%) | 31.03.2023 (%) |
|---|---|---|
| I. Equity and Liabilities | ||
| 1. Share Capital | (30,00,000 ÷ 50,00,000) × 100 = 60% | (10,00,000 ÷ 20,00,000) × 100 = 50% |
| 2. Long-term Borrowings | (16,00,000 ÷ 50,00,000) × 100 = 32% | (8,00,000 ÷ 20,00,000) × 100 = 40% |
| 3. Current Liabilities | (4,00,000 ÷ 50,00,000) × 100 = 8% | (2,00,000 ÷ 20,00,000) × 100 = 10% |
| Total | 100% | 100% |
| II. Assets | ||
| 1. Non-Current Assets (PPE & Intangibles) | (30,00,000 ÷ 50,00,000) × 100 = 60% | (14,00,000 ÷ 20,00,000) × 100 = 70% |
| 2. Current Assets (Inventory) | (20,00,000 ÷ 50,00,000) × 100 = 40% | (6,00,000 ÷ 20,00,000) × 100 = 30% |
| Total | 100% | 100% |
Interpretation:
In 2023, the company had a higher dependence on long-term assets (70%) and borrowed funds (40%).
In 2024, the company shifted towards greater equity financing (60%) and increased inventory (from 30% to 40%), suggesting expansion in operations and stock levels.
Current liabilities remained a small component across both years.
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 \(P,O,Q\).