Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of $$\frac{1}{400}{(\frac{100}{x}+x})$$ liters per km, when driven at the speed of x km per hour. If the cost of diesel is Rs. 35 per litre and the driver is paid at the rate of Rs. 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms.

SUV  consumes diesel at the rate of $$\frac{1}{400}{(\frac{100}{x}+x})$$ 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 $$\frac{1}{400}{(\frac{100}{x}+x})$$*35*800

Per hour Chargers of Driver is Rs. 125 and total time is $$\frac{800}{x}$$

Therefore total cost of driver is $$\frac{100000}{x}$$

Total Cost = $$\frac{100000}{x}$$ + $$\frac{1}{400}{(\frac{100}{x}+x})$$*35*800

               = $$\frac{107000}{x}$$ + 70x

We need total cost to be minimum so differentiating total cost w.r.t x and equating to 0 we get

0 = -$$\frac{107000}{x^2}$$ + 70

i.e. $$x^2$$ = $$\frac{107000}{70}$$

x = 39 approximately

Therefore option 'A' is the answer