The goods train between Bhilai to Lucknow without rakes can go upto the speed of 72km/hour, and the speed gets diminished by the quantity that varies as the square root of the number of wagons attached. If it is known that with 4 wagons the speed is 56 km/hour, the greatest number of wagons with which the engine can just move is:

Let the speed of the train be in the from $$S=72-k\sqrt{\ x}$$(since speed is proportional to the square root of the number of wagons).
Now, when the number of wagons is 4, the speed of the train is 56 km/hr.
Thus, $$56=72-k\sqrt{\ 4}$$
$$56=72-2k$$
$$k=8$$

Thus, $$S=72-8\sqrt{\ x}$$
Since speed cannot be negative,
$$S>0$$
$$72-8\sqrt{\ x}>0$$
$$\ x<81$$
The maximum value of x will be 80.
Thus, the correct option is D.