The speed of the rail engine is 42 km/hr when no compartment is attached.

Now, the reduction in speed (say ∆

*v*) is directly proportional to the square root of the number of compartments (say

*n*) attached.

[Here,

*k* is some positive constant]

∵ Reduction in speed of the train (∆

*v*) = 42 − 24 = 18 km/hr when 9 compartments are attached to the rail engine, so we get,

∴

*k* = 6

Let the number of compartments attached be

*x*, when the speed of the engine reduces to zero.

Therefore, reduction in speed of the rail engine = 42 − 0 = 42 km/hr

∴

*x* = 49

But when 49 compartments are attached, the speed of the engine reduces to zero,

∴ Maximum number of compartments should be one less than 49, i.e. 48, so that the rail engine can move.

Hence, option 1.