A locomotive engine can go 40 km/hr. Its speed gets reduced by a quantity that varies directly as the square root of the number of wagons attached. It is known that its speed becomes 16 km/hr if 36 wagons are attached. What is the smallest number of wagons with which the engine is unable to move?
A.100✓ Correct
B.81
C.64
D.49
Explanation
Speed = 40 - k√n where n is the number of wagons. With n = 36: 16 = 40 - k√36 = 40 - 6k, so 6k = 24, k = 4. Engine unable to move when speed ≤ 0: 40 - 4√n ≤ 0, so √n ≥ 10, i.e., n ≥ 100. Smallest such n is 100.
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