The following journal entry appears in the books of Latvion Ltd. : 
The discount on issue of debentures is :
To solve the problem, we need to determine the discount on the issue of debentures for Latvion Ltd., given the journal entry showing a debit of Rs 75,000 to 'Loss on Issue of Debentures A/c', a credit of Rs 5,00,000 to '12% Debentures A/c', a credit of Rs 50,000 to 'Premium on Redemption of Debentures A/c', and a debit of Rs 4,75,000 to 'Bank A/c'.
1. Understanding the Journal Entry:
The journal entry indicates the issuance of debentures. The nominal value of the debentures is Rs 5,00,000 (credited to 12% Debentures A/c). The company received Rs 4,75,000 in cash (debited to Bank A/c), and Rs 75,000 is debited to Loss on Issue of Debentures A/c, which includes the discount on issue and any premium on redemption. Rs 50,000 is credited to Premium on Redemption of Debentures A/c, indicating the premium payable on redemption.
2. Calculating the Discount on Issue:
The Loss on Issue of Debentures A/c is calculated as the discount on issue plus the premium on redemption. Let the discount on issue be \( D \). Then:
\( \text{Loss on Issue} = \text{Discount on Issue} + \text{Premium on Redemption} \)
Given:
\( 75,000 = D + 50,000 \)
Solving for \( D \):
\( D = 75,000 - 50,000 = 25,000 \, \text{Rs} \)
3. Determining the Discount Percentage:
The nominal value of the debentures is Rs 5,00,000. The discount on issue is Rs 25,000. The percentage discount is calculated as:
\( \text{Discount Percentage} = \left( \frac{\text{Discount}}{\text{Nominal Value}} \right) \times 100 \)
Substitute the values:
\( \text{Discount Percentage} = \left( \frac{25,000}{5,00,000} \right) \times 100 = 5\% \)
Final Answer:
The discount on the issue of debentures is 5%. The correct option is B.
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 \(P,O,Q\).