The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100 km/hr when there are 4 bogies and 55 km/hr when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that, even with those many numbers of bogies, it can just move?  Choose the correct choice from the following options.
A) 3
B) 4
C) 5
D) 6
E) 7
We know that S=Smax−K×(bogies)2   When there are 4 bogies speed of the train is 100km/hr 100=Smax−K×(4)2 ⇒100=Smax−K×16.......(1)   When there are 5 bogies speed of the train is 55km/hr   55=Smax−K×(5)2⇒ 55 = Smax−K×25 ........(2)   (2) - (1) gives 9K=45⇒K=5   By substituting K = 5 in either (1) or (2) we can find the maximum speed of the train = 180 km/hr   Assume, for N number of bogies the train does not move.   ⇒0=180−5(N)2⇒N=6   If the engine is attached to 6 bogies, it does not move. If we want the train to move we need to attach maximum of 5 bogies   Answer 5
<result>C</result>
The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100 km/hr when there are 4 bogies and 55 km/hr when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that, even with those many numbers of bogies, it can just move?