Calculate the Operating Ratio from the following information:
| Particulars | Amount (₹) |
|---|---|
| Revenue from Operations (Cash + Credit) | 25,00,000 |
| Purchases (Cash + Credit) | 12,00,000 |
| Carriage Inward | 20,000 |
| Salaries | 1,45,000 |
| Wages | 85,000 |
| Increase in Inventory | 50,000 |
Operating Ratio is calculated using the formula:
Operating Ratio = (Operating Cost / Revenue from Operations) × 100
Step 1: Calculate Cost of Goods Sold (COGS)
COGS = Purchases + Carriage Inward - Increase in Inventory
= 12,00,000 + 20,000 - 50,000 = 11,70,000
Step 2: Operating Expenses
Operating Expenses = Salaries + Wages
= 1,45,000 + 85,000 = 2,30,000
Step 3: Operating Cost
Operating Cost = COGS + Operating Expenses
= 11,70,000 + 2,30,000 = 14,00,000
Step 4: Calculate Operating Ratio
Operating Ratio = (14,00,000 / 25,00,000) × 100 = 56%
Answer: Operating Ratio = 56%
Balance Sheet of Madhavan, Chatterjee and Pillai as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Creditors | 1,10,000 | Cash at Bank | 4,05,000 |
| Outstanding Expenses | 17,000 | Stock | 2,20,000 |
| Mrs. Madhavan’s Loan | 2,00,000 | Debtors | 95,000 |
| Chatterjee’s Loan | 1,70,000 | Less: Provision for Doubtful Debts | (5,000) |
| Capitals: | Madhavan – 2,00,000 | Land and Building | 1,82,000 |
| Chatterjee – 1,00,000 | Plant and Machinery | 1,00,000 | |
| Pillai – 2,00,000 | |||
| Total | 9,97,000 | Total | 9,97,000 |
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Machinery | 7,00,000 | |
| Madhur | 9,00,000 | Investments | 4,00,000 |
| Neeraj | 8,00,000 | Debtors | 11,00,000 |
| Creditors | 6,00,000 | Stock | 2,00,000 |
| Bills Payable | 2,00,000 | Cash at Bank | 1,00,000 |
| Total | 25,00,000 | Total | 25,00,000 |
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 \(P,O,Q\).