Discussion

Explanation:

Without any wagons, the speed is 240 km/hr. The speed diminishes by a quantity that varies (directly) as the square root of the number of wagons attached (∵ By default, variation is direct).

Let the quantity (by which the speed diminishes) be Q, the number of wagons attached be N.

Q ∝ √N

∴ Q = k√N

When Q = 240 – 100 = 140, N = 49. ∴ k = 20

When the train can just move, its speed = 240 – 20√N, would be slightly more than 0.

∴ 240 – 20√N > 0

∴ √N < 12.

∴ N < 144

∴ The greatest value of N is 143.    

Hence, option (c).

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