Step 1: Correct Interest on Capital (as per deed @ 8%)
Jay = ₹9,00,000 × 8% = ₹72,000
Vijay = ₹7,00,000 × 8% = ₹56,000
Step 2: Interest on Capital Already Given (@ 9%)
Jay = ₹9,00,000 × 9% = ₹81,000
Vijay = ₹7,00,000 × 9% = ₹63,000
Step 3: Excess Interest Allowed (to be withdrawn)
Jay = ₹81,000 - ₹72,000 = ₹9,000 (excess)
Vijay = ₹63,000 - ₹56,000 = ₹7,000 (excess)
Total excess allowed = ₹9,000 + ₹7,000 = ₹16,000
Step 4: Excess should have been distributed in 7:3 ratio
Jay’s correct share of ₹16,000 = \( \frac{7}{10} \times 16,000 = ₹11,200 \)
Vijay’s correct share of ₹16,000 = \( \frac{3}{10} \times 16,000 = ₹4,800 \)
Step 5: Compare actual vs. correct share
- Jay received ₹9,000 but was entitled to ₹11,200 → Short by ₹2,200
- Vijay received ₹7,000 but was entitled to ₹4,800 → Excess by ₹2,200
Step 6: Rectifying Journal Entry
| Particulars | Dr. (₹) | Cr. (₹) |
|---|---|---|
| Vijay’s Capital A/c | 2,200 | |
| To Jay’s Capital A/c | 2,200 | |
| (Being excess interest on capital allowed to Vijay transferred to Jay) | ||
| Particulars | Debit Amount (₹) | Credit Amount (₹) |
|---|---|---|
| (A) No Entry | ||
| (B) Sun’s Current A/c Dr. To Moon’s Current A/c | 50,000 | 50,000 |
| (C) Moon’s Current A/c Dr. To Sun’s Current A/c | 50,000 | 50,000 |
| (D) Sun’s Current A/c Dr. Moon’s Current A/c Dr. To Profit and Loss Appropriation A/c | 50,000 50,000 | 1,00,000 |
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 \(P,O,Q\).