

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: Calculate Operating Expenses
Operating Expenses = Salaries + Wages
= ₹1,45,000 + ₹85,000 = ₹2,30,000
Step 3: Calculate Operating Cost
Operating Cost = COGS + Operating Expenses
= ₹11,70,000 + ₹2,30,000 = ₹14,00,000
Step 4: Calculate Operating Ratio
Operating Ratio = (Operating Cost / Revenue from Operations) × 100
= (₹14,00,000 / ₹25,00,000) × 100 = 56%
Step 1: Start with Net Profit before Tax
Change in Statement of Profit and Loss = Closing – Opening
= ₹5,00,000 – ₹12,00,000 = (₹7,00,000) (Net Loss)
Add: Non-cash and Non-operating Expenses
Depreciation = ₹5,00,000 – ₹3,00,000 = ₹2,00,000
Loss on sale of machinery = ₹70,000
Total Adjustments = ₹2,00,000 + ₹70,000 = ₹2,70,000
Adjusted Operating Loss before Working Capital Changes
= (₹7,00,000) + ₹2,70,000 = (₹4,30,000)
Step 2: Adjust for Changes in Working Capital
Inventories: No change = ₹0
Trade Receivables: ₹10,00,000 – ₹2,00,000 = ₹8,00,000 (Increase) ⇒ Decrease in cash
Trade Payables: ₹5,00,000 – ₹3,50,000 = ₹1,50,000 (Increase) ⇒ Increase in cash
Net change in working capital = –₹8,00,000 + ₹1,50,000 = –₹6,50,000
Cash used in Operating Activities
= (₹4,30,000) – ₹6,50,000 = –₹10,80,000
Final Answer: Net Cash used in Operating Activities = –₹10,80,000
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 \(P,O,Q\).