Rishika and Shivika were partners in a firm sharing profits and losses in the ratio of 3 : 2. Their Balance Sheet as at 31st March, 2024 stood as follows:
Balance Sheet of Rishika and Shivika as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Equipment | 45,00,000 | |
| Rishika – ₹30,00,000 Shivika – ₹20,00,000 | 50,00,000 | Investments | 5,00,000 |
| Shivika’s Husband’s Loan | 5,00,000 | Debtors | 35,00,000 |
| Creditors | 40,00,000 | Stock | 8,00,000 |
| Cash at Bank | 2,00,000 | ||
| Total | 95,00,000 | Total | 95,00,000 |
The firm was dissolved on the above date and the following transactions took place:
(i) Equipements were given to creditors in full settlement of their account.
(ii) Investments were sold at a profit of 20% on its book value.
(iii) Full amount was collected from debtors.
(iv) Stock was taken over by Rishika at 50% discount.
(v) Actual expenses of realisation amounted to ₹ 2,00,000 which were paid by the firm. Prepare Realisation Account.
| Dr. | ₹ | Cr. | ₹ | |
|---|---|---|---|---|
| To Equipment A/c | 45,00,000 | By Creditors A/c (settled by equipment) | 40,00,000 | |
| To Investments A/c | 5,00,000 | By Bank A/c (Investment realised ₹6,00,000) | 6,00,000 | |
| To Debtors A/c | 35,00,000 | By Bank A/c (Debtors realised) | 35,00,000 | |
| To Stock A/c | 8,00,000 | By Rishika’s Capital A/c (Stock taken at 50%) | 4,00,000 | |
| To Bank A/c (Realisation Expenses) | 2,00,000 | By Loss on Realisation (shared in 3:2) | ||
| Rishika’s Capital A/c | 2,40,000 | |||
| Shivika’s Capital A/c | 1,60,000 | |||
| Total | 95,00,000 | Total | 95,00,000 |
Final Answer: Loss on Realisation = ₹4,00,000
Rishika’s Share (3/5) = ₹2,40,000
Shivika’s Share (2/5) = ₹1,60,000
Manav and Namit were partners in a firm sharing profits and losses in the ratio of 3 : 2. Their Balance Sheet as at 31st March 2024 was as follows:
| Liabilities | Assets | ||
|---|---|---|---|
| Capitals: | Machinery | ₹8,00,000 | |
| Manav | ₹4,00,000 | Investments | ₹5,00,000 |
| Namit | ₹6,00,000 | Debtors | ₹12,00,000 |
| Bank Overdraft | ₹9,00,000 | Stock | ₹3,00,000 |
| Creditors | ₹10,00,000 | Cash in Hand | ₹1,00,000 |
| Total | ₹29,00,000 | Total | ₹29,00,000 |
The firm was dissolved on the above date and the following transactions took place:
[(i)] Stock was given to creditors in full settlement of their account.
[(ii)] Investments were taken over by Manav at 120% of book value.
[(iii)] Bad debts amounted to ₹ 2,00,000.
[(iv)] Machinery was realised at 50% discount.
[(v)] Realisation expenses amounted to ₹ 1,00,000 which were paid by Namit.
Prepare Realisation Account.
Match List-I with List-II:\[\begin{array}{|c|c|} \hline \text{List-I} & \text{List-II} \\ \hline \text{(A) Compulsory Dissolution} & \text{(I) Partner becomes insane} \\ \hline \text{(B) Dissolution by notice} & \text{(II) Death of a partner} \\ \hline \text{(C) Dissolution by Court} & \text{(III) Business becomes illegal} \\ \hline \text{(D) Dissolution on certain contingencies} & \text{(IV) Partnership at will} \\ \hline \end{array}\]Choose the correct answer from the options given below:
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 \(P,O,Q\).