Multiple choice

Two trains with V1, V2 speeds take 3 seconds to pass one another when going in opposite direction, but take only 2.5 seconds if the speed of any one of it is increase by (its speed) 50%. The time one would take to pass the other when going in the same direction with V1, V2 speeds is ______ sec. [NTSE - Stage - 1, 2018-19, Andhra Pradesh]

  1. 10

  2. 18

  3. 15

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let lengths be L1, L2. V1+V2 = (L1+L2)/3. If one speed increases by 50%, say V1 becomes 1.5V1, then 1.5V1+V2 = (L1+L2)/2.5. This implies 1.5V1+V2 = 1.2(V1+V2), so 1.5V1+V2 = 1.2V1+1.2V2, 0.3V1 = 0.2V2, V2 = 1.5V1. Substituting back, L1+L2 = 3(V1+1.5V1) = 7.5V1. Time same direction = (L1+L2) / |V1-V2| = 7.5V1 / 0.5V1 = 15.

AI explanation

Let the relative speed in opposite directions be (V1 + V2) and the sum of their lengths be D. We have D = 3(V1 + V2). If one speed increases by 50%, the new relative speed becomes (1.5V1 + V2), and we are given D = 2.5(1.5V1 + V2). Setting the equations equal gives 3V1 + 3V2 = 3.75V1 + 2.5V2, which simplifies to 0.5V2 = 0.75V1, or V2 = 1.5V1. Substituting this back, D = 7.5V1. In the same direction, the relative speed is (V2 - V1) = 0.5V1, so the time taken is D / 0.5V1 = 7.5V1 / 0.5V1 = 15 seconds. The result is 15.

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