Indian Institute of Foreign Trade 2009 Solved Paper

SUV consumes diesel at the rate of $\frac{1}{400}\left(\frac{100}{\mathit{x}}+\mathit{x}\right)$ liters per km
Cost of 1 liter diesel is Rs. 35
Total distance to be covered is 800 kms
Therefore total cost of diesel consumption by SUV is $\frac{1}{400}\left(\frac{100}{\mathit{x}}+\mathit{x}\right)\times 35\times 800$
Per hour Chargers of Driver is Rs. 125 and total time is $\frac{800}{\mathit{x}}$
Therefore total cost of driver is $\frac{100000}{\mathit{x}}$
Total Cost $=\frac{100000}{\mathit{x}}+\frac{1}{400}\left(\frac{100}{\mathit{x}}+\mathit{x}\right)\times 35\times 800$
$=\frac{10700}{\mathit{x}}+70\mathit{x}$
We need total cost to be minimum so differentiating total cost w.r.t x and equating to 0 we get
$0=-\frac{107000}{{\mathit{x}}^2}+70$
i.e, ${\mathit{x}}^2=\frac{107000}{70}$
x = 12 approximately
Therefore option 'A' is the answer