1. Total profit of the firm = rupee 1,10,000
2. Profit-sharing ratio (Mahi: Ruhi: Ginni) = 6:4:1
3. Distribution of profit as per the ratio: \[\text {Mahi’s share} = \frac{6}{11} \times 1,10,000 = rupee 60,000 \] \[ \text{Ruhi’s share} = \frac{4}{11} \times 1,10,000 = rupee 40,000 \] \[ \text{Ginni’s share} = \frac{1}{11} \times 1,10,000 = rupee 10,000 \]
4. Guaranteed profit for Ginni = rupee 50,000. However, Ginni’s share from the distribution is only rupee 10,000.
- Deficiency to be paid by Mahi = \( 50,000 - 10,000 = 40,000 \).
- This amount is deducted from Mahi’s share.
5. Final share of Mahi after adjusting the guarantee: \[ \text{Mahi’s final profit} = rupee 60,000 - rupee 40,000 = rupee 20,000. \]
Thus, the correct answer is rupee20,000 (Option A).

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 \(P,O,Q\).