Step 1: Key Details –
Amount due to Rohit = ₹ 6,00,000
Instalments = 4 equal yearly instalments = ₹ 1,50,000 per year
Interest = 9% p.a. on reducing balance
Payment starts from: 31st March, 2021
Step 2: Rohit's Loan Account
| Date | Particulars | Amount (₹) | Date | Particulars | Amount (₹) |
|---|---|---|---|---|---|
| 2021 Mar 31 | Interest A/c | 54,000 | 2021 Mar 31 | Bank A/c | 1,50,000 |
| Balance c/d | 5,04,000 | ||||
| 2022 Mar 31 | Interest A/c | 45,360 | 2022 Mar 31 | Bank A/c | 1,50,000 |
| Balance c/d | 3,99,360 | ||||
| 2023 Mar 31 | Interest A/c | 35,942 | 2023 Mar 31 | Bank A/c | 1,50,000 |
| Balance c/d | 2,85,302 | ||||
| 2024 Mar 31 | Interest A/c | 25,677 | 2024 Mar 31 | Bank A/c | 3,10,979 |
Calculation Breakdown:
Year 1 interest = 9% of ₹6,00,000 = ₹54,000
Year 2 interest = 9% of ₹5,04,000 = ₹45,360
Year 3 interest = 9% of ₹3,99,360 = ₹35,942
Year 4 interest = 9% of ₹2,85,302 = ₹25,677
Final payment = Principal + Last year’s interest = ₹2,85,302 + ₹25,677 = ₹3,10,979

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 \(P,O,Q\).