On 1st April, 2024, Varsha Ltd. purchased from Rama Ltd., furniture at 12,00,000 and machinery at 20,00,000. It also took over its liabilities amounting to 3,00,000. The purchase consideration of 35,00,000 was paid by issuing a bank draft of 2,00,000 and the balance by issue of 11% Debentures of 100 each, at a premium of 10%.
Pass necessary journal entries for the above transactions in the books of Varsha Ltd.
Step 1: Total purchase consideration = 35,00,000
Step 2: Payment made:
- By Bank Draft = 2,00,000
- Balance = 33,00,000 to be paid via 11% Debentures at 10% premium.
Face value per debenture = 100; Issue price = 110 \[ \text{Number of debentures} = \frac{33,00,000}{110} = 30,000 \text{ debentures} \] Step 3: Assets taken over:
- Furniture = 12,00,000
- Machinery = 20,00,000
- Liabilities = 3,00,000 (to be credited)
Journal Entries:
1. For purchase of assets and liabilities: Furniture A/c Dr. & 12,00,000
Machinery A/c Dr. & 20,00,000
To Liabilities A/c & 3,00,000
To Rama Ltd. & 29,00,000
2. For payment of purchase consideration: Rama Ltd. A/c Dr. & 35,00,000
To Bank A/c & 2,00,000
To 11% Debentures A/c & 30,00,000
To Securities Premium A/c & 3,00,000
Note: \(30,000 \text{ debentures} \times 100 = 30,00,000\) (face value)
Premium = \(30,000 \times 10 = 3,00,000\)
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 \(P,O,Q\).