Algebra
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Q.

The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached.

If the speed of the train carried by this engine is 24 Km per hour with 9 compartments are attached, the maximum number of compartments carried by the engine is:

 A.

46

 B.

47

 C.

48

 D.

49

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Solution:
Option(C) is correct

\(24= 42- k \sqrt{9}\\ \Rightarrow k \sqrt{9}=18\\ \Rightarrow k=6\)

\(0=42-6\sqrt{x}\) (because maximum number of compartments that can be carried can be obtained by finding when the speed is zero and subtracting one from it).

\(42= 6 \sqrt{x}\\ \Rightarrow x=49\)

\(\therefore\) maximum number of compartments carried by engine,

\(=49 - 1\\ = \textbf{48}\)


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Brayan Hernandez
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