The reduction in speed of a locomotive engine is directly proportional to square root of no. of wagons attached to it. Speed of engine was 240 km/hr when no wagons were attached to it. When 49 wagons were attached the speed became 100 km/hr. Maximum how many wagons can be attached to engine such that engine keeps on moving?
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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