1. Total amount received on reissue of 70 shares \[ = 70 \times rupee 10 = rupee 700 \]
2. Total amount originally called up before reissue \[ = 70 \times rupee 8 = rupee 560 \]
3. Gain on reissue calculation \[ \text{Gain on Reissue} = \text{Reissue Amount} - \text{Called-up Amount} \] \[ = rupee 700 - rupee 560 = rupee 140 \]
4. Forfeited amount per share before reissue The amount forfeited per share:
- Total amount called up = rupee 8 (excluding final call)
- Paid by Ramesh = Application Money (rupee 3)
- Unpaid by Ramesh = Allotment Money (rupee 5)
- Premium amount (rupee 2) was included in allotment but not received (hence not part of forfeiture balance)
- Amount forfeited per share = rupee3
- Total forfeited amount for 70 shares = \( 70 \times 3 = rupee 210 \)
5. Final Gain on Reissue \[ \text{Total Gain} = \text{Reissue Gain} + \text{Forfeited Amount} \] \[ = rupee 140 + rupee 210 = rupee 350 \] Thus, the correct answer is rupee350 (Option C).
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 \(P,O,Q\).