Step 1: Calculate Sale Value of Machinery Sold
Cost of machinery sold = Rs. 1,40,000
Less: Accumulated Depreciation = Rs. 90,000
$\Rightarrow$ Book Value = Rs. 50,000
Gain on sale = Rs. 10,000
$\Rightarrow$ Sale Price = Rs. 50,000 + Rs. 10,000 = Rs. 60,000
Step 2: Calculate Purchase of Machinery
Let machinery purchased = Rs. $x$
Opening Gross Block = Rs. 50,00,000
Less: Cost of machinery sold = Rs. 1,40,000
Add: Purchases = $x$
Closing Gross Block = Rs. 70,00,000
$70,00,000 = 50,00,000 - 1,40,000 + x \Rightarrow x = 21,40,000$
Step 3: Calculate Cash Flow from Investing Activities
Outflow: Purchase of Machinery = Rs. 21,40,000
Inflow: Sale of Machinery = Rs. 60,000
$\textbf{Net Cash Used in Investing Activities} = 21,40,000 - 60,000 = Rs. 20,80,000$
Final Answer:
$\boxed{\text{Cash Used in Investing Activities} = \text{Rs. } 20,80,000}$
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 \(P,O,Q\).