Multiple choice

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. 1 : 4

  2. 7 : 5

  3. 5 : 7

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance AB = d, then BC = 3d. Train 1 speed on AB = v, on BC = 2v. Train 2 speed on AB = 2v, on BC = v. Time for T1 = d/v + 3d/2v = 5d/2v. Time for T2 = d/2v + 3d/v = 7d/2v. Ratio T1:T2 = 5:7.

AI explanation

Let the distance from A to B be d, making the distance from B to C equal to 3d, and let the speeds of train 1 and train 2 be v and 2v, respectively. The total time for train 1 is (d/v) + (3d/2v), which equals 5d/2v. The total time for train 2 is (d/2v) + (3d/v), which equals 7d/2v. The ratio of their times is (5d/2v) : (7d/2v), resulting in 5 : 7.

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