
On 31st March, 2024, Arti retired from the firm. Revaluation Account and Partners’ Capital Accounts will be prepared after incorporating the following adjustments:
(i) Goodwill of the firm was valued at ₹~3,00,000.
(ii) Provision of 5% for doubtful debts on ₹~70,000 = ₹~3,500
(iii) Machinery depreciation 10% on ₹~1,40,000 = ₹~14,000
Appreciation in Building by ₹~22,500
(iv) Patents ₹~5,000 written off
(v) Claim admitted for workmen compensation ₹~15,000
Revaluation Account:
To Machinery Depreciation ............................ ₹~14,000
To Provision for Doubtful Debts .................... ₹~3,500
To Patents Written Off ................................. ₹~5,000
To Workmen Compensation Claim ........... ₹~15,000
Total Losses ........................................... ₹~37,500
By Building Appreciation ............................ ₹~22,500
Net Loss Transferred to Partners (5:3:2):
Arti ........................ ₹~7,500
Bharti .................... ₹~4,500
Gayatri .................. ₹~3,000
Goodwill Adjustment:
Arti’s share of goodwill = ₹~3,00,000 × $ \dfrac{5}{10} $ = ₹~1,50,000
Gaining Ratio of Bharti and Gayatri (3:2):
Bharti = ₹~90,000, Gayatri = ₹~60,000
Partners’ Capital Accounts (Summary Effects):
Arti:
Opening Capital = ₹~2,00,000
(+) General Reserve = ₹~65,000 ($ \dfrac{5}{10} $ of ₹~1,30,000)
(+) Employees’ PF = ₹~12,500 ($ \dfrac{5}{10} $ of ₹~25,000)
(+) Workmen Compensation Fund = ₹~37,500 ($ \dfrac{5}{10} $ of ₹~75,000)
(–) Revaluation Loss = ₹~7,500
(–) Share of P&L Loss = ₹~40,000 ($ \dfrac{5}{10} $ of ₹~80,000)
(–) Goodwill Adjustment = ₹~1,50,000
Closing Capital = Sum of above adjustments = Final Settlement Due
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 \(P,O,Q\).