Usha and Mohak were partners in a firm. Usha withdrew a fixed amount at the end of every half-year for the year ended 31st March, 2024. Interest on drawings is charged at 9% p.a. Interest on Usha’s drawings will be charged for months.
Step 1: Usha withdrew a fixed amount at the end of every half-year. That means she withdrew twice in the year:
- First withdrawal at the end of September 2023
- Second withdrawal at the end of March 2024
Step 2: Interest on drawings is calculated for the period from date of withdrawal till the end of the financial year.
Step 3: Interest is charged as follows:
- For withdrawal on 30th September, interest = 6 months (Oct to Mar)
- For withdrawal on 31st March, interest = 0 months
Step 4: Average period = \( \frac{6 + 0}{2} = 3 \) months
Interest on drawings will be charged for 3 months.
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 \(P,O,Q\).