Ratio of Train Travel Times

CAT 2020 Slot 2 · QA · Easy · Arithmetic

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The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is

  1. A.

    7:5

  2. B.

    4:1

  3. C.

    1:4

  4. D.

    5:7

Answer

D

Explanation

Let AB=dAB = d, then BC=3dBC = 3d. Let speed of train 1 from A to B be vv, then speed of train 2 from A to B is 2v2v. From B to C, speed of train 1 is 2v2v and speed of train 2 is vv.

Time taken by train 1: t1=dv+3d2v=5d2vt_1 = \frac{d}{v} + \frac{3d}{2v} = \frac{5d}{2v} Time taken by train 2: t2=d2v+3dv=7d2vt_2 = \frac{d}{2v} + \frac{3d}{v} = \frac{7d}{2v}

Ratio t1:t2=5d/2v7d/2v=5:7t_1 : t_2 = \frac{5d/2v}{7d/2v} = 5 : 7.

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