The Howrah-Puri express can move at 45 km/hour without its rake, and the speed is diminished by a constant that varies as the square root of the number of wagons attached. If it is known that with 9 wagons, the speed is 30 km/hour, what is the greatest number of wagons with which the train can just move?

Given that, $$(45-x) \ltimes \sqrt{n} $$
=> $$(45-x) = k*\sqrt{n} $$
Where x is the speed of the train, k is the proportionality constant and n is the number of wagon wheels attached.
Now given that when n = 9, x= 30
Thus, $$ 15 = k*3 $$
thus, k = 5
Thus, $$ 45-x = 5\sqrt{n} $$
Thus, when n = 81 x = 0
Thus, for the train to move the maximum number of wagon wheels = 80
Hence, option C is the correct answer.