Step 1: Calculate profit shares in the ratio 5 : 3 : 8
Total ratio = \( 5 + 3 + 8 = 16 \)
Aman’s share = \( \frac{5}{16} \times 8,00,000 = ₹2,50,000 \)
Raj’s share = \( \frac{3}{16} \times 8,00,000 = ₹1,50,000 \)
Suresh’s share = \( \frac{8}{16} \times 8,00,000 = ₹4,00,000 \)
Step 2: Apply minimum guarantee
Suresh was guaranteed ₹5,00,000 but got only ₹4,00,000
Deficiency = ₹5,00,000 – ₹4,00,000 = ₹1,00,000
To be borne equally by Aman and Raj
So, Aman’s sacrifice = ₹50,000
Raj’s sacrifice = ₹50,000
Final adjusted shares:
Aman = ₹2,50,000 – ₹50,000 = ₹2,00,000
Raj = ₹1,50,000 – ₹50,000 = ₹1,00,000
Suresh = ₹4,00,000 + ₹1,00,000 = ₹5,00,000
Profit and Loss Appropriation Account for the year ended 31st March, 2024
| Dr. | Cr. | ||
|---|---|---|---|
| Particulars | Amount (₹) | Particulars | Amount (₹) |
| To Aman’s Capital A/c | ₹2,00,000 | By Net Profit | ₹8,00,000 |
| To Raj’s Capital A/c | ₹1,00,000 | ||
| To Suresh’s Capital A/c | ₹5,00,000 | ||
| Total | ₹8,00,000 | Total | ₹8,00,000 |
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 \(P,O,Q\).