2026 · Q34
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?
Elementary MathematicsRatio and Proportion
- A100
- B81
- C64
- D49
Explanation
Model the speed as 40−k√n; from 16=40−6k we get k=4. The engine cannot move once 40−4√n≤0, i.e. n≥100, so the smallest such number of wagons is 100, option A.