Given:
Profit sharing ratio = 3 : 2 : 1
Aman's guaranteed minimum profit = ₹60,000
Net Profit for the year = ₹1,20,000
Step 1: Calculate normal share of profit:
Total ratio = 3 + 2 + 1 = 6
Chaman's share = ₹1,20,000 × (3/6) = ₹60,000
Burman's share = ₹1,20,000 × (2/6) = ₹40,000
Aman's share = ₹1,20,000 × (1/6) = ₹20,000
Step 2: Check Aman’s guarantee:
Aman is guaranteed ₹60,000 but he has got only ₹20,000.
Deficiency = ₹60,000 − ₹20,000 = ₹40,000.
Step 3: Deficiency borne by Chaman and Burman in their profit-sharing ratio (3:2):
Chaman’s share of deficiency = ₹40,000 × (3/5) = ₹24,000
Burman’s share of deficiency = ₹40,000 × (2/5) = ₹16,000
Step 4: Adjusted profit distribution:
Chaman = ₹60,000 − ₹24,000 = ₹36,000
Burman = ₹40,000 − ₹16,000 = ₹24,000
Aman = ₹20,000 + ₹40,000 = ₹60,000
Step 5: Journal Entries:
| Date | Particulars | Debit (₹) | Credit (₹) |
|---|---|---|---|
| 31-Mar-2023 | Profit and Loss A/c Dr. To Chaman’s Capital A/c To Burman’s Capital A/c To Aman’s Capital A/c (Being net profit transferred to partners’ capital accounts in their profit-sharing ratio) | 1,20,000 | Chaman: 60,000 Burman: 40,000 Aman: 20,000 |
| 31-Mar-2023 | Chaman’s Capital A/c Dr. 24,000 Burman’s Capital A/c Dr. 16,000 To Aman’s Capital A/c 40,000 (Being deficiency in Aman’s guaranteed profit borne by Chaman and Burman in 3:2 ratio) | 40,000 | 40,000 |
Final Profit Distribution:
Chaman: ₹36,000
Burman: ₹24,000
Aman: ₹60,000
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 \(P,O,Q\).