| Date | Particulars | L.F. | Dr. (₹) | Cr. (₹) |
|---|---|---|---|---|
| Equity Share Capital A/c Dr. (750 × ₹10) Securities Premium A/c Dr. (750 × ₹1) To Share Forfeiture A/c To Calls-in-Arrears A/c (Being 750 shares forfeited for non-payment of first call of ₹3 per share including ₹1 premium) | 7,500 750 | 6,000 2,250 | ||
| Bank A/c Dr. Share Forfeiture A/c Dr. To Equity Share Capital A/c (500 × ₹10) To Securities Premium A/c (Being 500 forfeited shares re-issued at ₹5 per share as ₹7 paid-up) | 2,500 1,000 | 5,000 500 | ||
| Share Forfeiture A/c Dr. To Capital Reserve A/c (Being profit on re-issue transferred to Capital Reserve) | 3,000 | 3,000 |
Face Value per Share = ₹10 Total Premium per Share = ₹1 First Call per Share = ₹3 (including ₹1 premium) Second & Final Call per Share = ₹3 (not yet called) Amount called up before forfeiture: \[ 11 - 3 = 8 \text{ per share} \] ---
Amount received per share = ₹8 \[ 750 \times 8 = 6,000 \] So Share Forfeiture A/c credited = ₹6,000 ---
Called-up capital: \[ 750 \times 10 = 7,500 \] Premium unpaid: \[ 750 \times 1 = 750 \] First call unpaid: \[ 750 \times 3 = 2,250 \] Amount received: \[ 750 \times 8 = 6,000 \] ---
Re-issue price: \[ 500 \times 5 = 2,500 \] Share Forfeiture available for 500 shares: \[ \frac{500}{750} \times 6,000 = 4,000 \] Discount on re-issue: \[ 1,000 \] ---
Share Forfeiture balance before re-issue = ₹6,000 Less: Discount on re-issue = ₹1,000 Less: Balance relating to 250 shares: \[ \frac{250}{750} \times 6,000 = 2,000 \] Amount transferred: \[ 6,000 - 1,000 - 2,000 = 3,000 \]
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 \(P,O,Q\).