
Formula:
Proprietary Ratio = Shareholders' Funds / Total Assets
| Particulars | Amount (₹) |
|---|---|
| Equity Share Capital | 3,00,000 |
| Preference Share Capital | 1,00,000 |
| Reserves and Surplus | 1,00,000 |
| Shareholders' Funds | 5,00,000 |
| Particulars | Amount (₹) |
|---|---|
| Plant and Machinery | 3,50,000 |
| Non-Current Investments | 1,00,000 |
| Current Assets | 2,00,000 |
| Total Assets | 6,50,000 |
Proprietary Ratio = 5,00,000 / 6,50,000
Proprietary Ratio = 0.77 : 1 (approximately)
Formula:
Debt-to-Equity Ratio = Long Term Debts / Shareholders' Funds
| Particulars | Amount (₹) |
|---|---|
| Long-term Borrowings | 1,50,000 |
| Long Term Debts | 1,50,000 |
Shareholders' Funds = ₹ 5,00,000
Debt-to-Equity Ratio = 1,50,000 / 5,00,000
Debt-to-Equity Ratio = 0.30 : 1
| Ratio | Value |
|---|---|
| Proprietary Ratio | 0.77 : 1 |
| Debt-to-Equity Ratio | 0.30 : 1 |
A Proprietary Ratio of 0.77 : 1 indicates that 77% of total assets are financed by shareholders’ funds.
A Debt-to-Equity Ratio of 0.30 : 1 shows that for every ₹1 of shareholders’ funds, the company has ₹0.30 of long-term debt. This reflects low financial leverage and a strong equity position.
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 \(P,O,Q\).