Aditi’s capital is ₹5,00,000, and the interest rate is \(10\% \text{ p.a.}\). However, if the interest is calculated for 9 months instead of the full year, the calculation becomes: \[ \text{Interest on Capital} = ₹5,00,000 \times 10\% \times \frac{9}{12}. \]
Step 1: Calculate annual interest:
Annual interest = \( ₹5,00,000 \times 10\% = ₹50,000. \)
Step 2: Adjust for 9 months:
Interest for 9 months: \[ ₹50,000 \times \frac{9}{12} = ₹45,000. \]
Conclusion:
The interest on Aditi’s capital for 9 months is \( ₹45,000 \).
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 \(P,O,Q\).