To determine the profit credited to Farida's capital account, we need to compare her guaranteed profit with what she would receive based on the profit-sharing ratio.
Step 1: Determine the actual profit for each partner based on the profit-sharing ratio.
Total profit earned by the firm = Rs 80,000.
Profit-sharing ratio is 4:3:1 for Emily, Farida, and Gauri.
| Partner | Ratio | Share of Profit |
|---|---|---|
| Emily | 4 | (4/8) × 80,000 = Rs 40,000 |
| Farida | 3 | (3/8) × 80,000 = Rs 30,000 |
| Gauri | 1 | (1/8) × 80,000 = Rs 10,000 |
Step 2: Compare Farida's actual profit share to her guaranteed amount.
Guaranteed profit for Farida = Rs 35,000.
Actual profit credited, based on ratio = Rs 30,000.
Step 3: Calculate deficiency and ensure guaranteed amount is met.
Deficiency = Guaranteed amount - Actual share = Rs 35,000 - Rs 30,000 = Rs 5000.
Emily is to cover any deficiency for Farida. Therefore, an additional Rs 5000 will be transferred from Emily's share to Farida's.
Conclusion: Profit credited to Farida's capital account = Rs 30,000 + Rs 5000 = Rs 35,000.
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 \(P,O,Q\).