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 ✓
- B. 81
- C. 64
- D. 49
Correct Answer: A. 100
Explanation
Reduction in speed R = k\sqrt{n}. With 36 wagons, speed drops from 40 to 16, so R = 24. Thus, 24 = k\sqrt{36} \implies 6k = 24 \implies k = 4. For the engine to be unable to move, R must be 40. Solving 40 = 4\sqrt{n} gives \sqrt{n} = 10, so n = 100.
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