CDS 2026 (I) Elementary Mathematics, question 34

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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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 ?

  1. (a) 100100Correct answer
  2. (b) 8181
  3. (c) 6464
  4. (d) 4949

Solution.

Answer: (a) 100100

  1. Model the speed as v=40−cnv = 40 - c\sqrt{n}.
  2. At n=36,16=40−6cn = 36,16 = 40 - 6c, so c=4c = 4.
  3. The engine cannot move once 40−4n≤040 - 4\sqrt{n} \leq 0, which requires n≥100n \geq 100.