Step 1: Interest on Capital
Jain:
Capital before withdrawal = ₹15,00,000
Withdrawal on 1st July = ₹1,00,000
Capital from 1st April to 30th June (3 months) = ₹15,00,000
Capital from 1st July to 31st March (9 months) = ₹14,00,000
Interest = \( (15,00,000 \times 10% \times \frac{3}{12}) + (14,00,000 \times 10% \times \frac{9}{12}) \)
⇒ ₹37,500 + ₹1,05,000 = ₹1,42,500
Gupta:
Original capital = ₹12,00,000
Additional capital on 1st July = ₹2,00,000
Interest = \( (12,00,000 \times 10% \times \frac{12}{12}) + (2,00,000 \times 10% \times \frac{9}{12}) \)
⇒ ₹1,20,000 + ₹15,000 = ₹1,35,000
Step 2: Interest on Drawings
Drawings of Jain = ₹50,000
Assumed withdrawn evenly → interest for 6 months
Interest = \( 50,000 \times 18% \times \frac{6}{12} = ₹4,500 \)
Drawings of Gupta = ₹60,000
Interest = \( 60,000 \times 18% \times \frac{6}{12} = ₹5,400 \)
Step 3: Profit Share (already given)
Jain = ₹72,000
Gupta = ₹48,000
Step 4: Prepare Current Accounts
Jain’s Current Account
| Credit Side | Debit Side |
|---|---|
| By Interest on Capital: ₹1,42,500 | To Drawings: ₹50,000 |
| By Share of Profit: ₹72,000 | To Interest on Drawings: ₹4,500 |
| Total Cr = ₹2,14,500 | Total Dr = ₹54,500 |
| Closing Balance = ₹1,60,000 | |
Gupta’s Current Account
| Credit Side | Debit Side |
|---|---|
| By Interest on Capital: ₹1,35,000 | To Drawings: ₹60,000 |
| By Share of Profit: ₹48,000 | To Interest on Drawings: ₹5,400 |
| Total Cr = ₹1,83,000 | Total Dr = ₹65,400 |
| Closing Balance = ₹1,17,600 | |
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 \(P,O,Q\).