Question 19

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, $$56=72-k\sqrt{\ 4}$$

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

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