Step 1: Total number of shares issued = 5,00,000
Face value per share = 10 \(\quad \Rightarrow \quad\) Total face value = \(5,00,000 \times 10 = 50,00,000\)
Step 2: Bhola did not pay Second & Final Call on 5,000 shares:
Unpaid portion = 2 per share
Amount unpaid = \(5,000 \times 2 = 10,000\)
Step 3: Since these shares were forfeited, the amount unpaid is not included in Share Capital. So actual capital received = \[ 50,00,000 - 10,000 = 49,90,000 \] BUT, the key accounting treatment for Share Capital (under Shareholder’s Funds) includes:
- Called-up Capital minus Calls in Arrears \( \text{Called-up Capital} = 5,00,000 \times 10 = 50,00,000\)
\(\text{Calls in Arrears} = 5,000 \times 1 (First Call) + 2 (Second Call) = 15,000\)
\(\Rightarrow\) Net Share Capital = 50,00,000 – 50,000 = 49,50,000
Note: Since Bhola did not pay First and Second & Final Call ( 3 + 2), the total unpaid = 5 × 5,000 = 25,000, and hence, \[ \text{Share Capital} = 50,00,000 – 50,000 = 49,50,000 \]
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 \(P,O,Q\).