CDS 2025 · PYQ · Trains / Time, Speed and Distance · medium
A train of certain length takes time t to pass completely through a station of length x. The same train with same speed takes time 2t to pass completely through another station of length y. What is the time taken by the train to pass completely through a station of length (x + y)?
A.(2yt + xt) / (y - x)
B.(yt + xt) / (y - x)
C.(3yt - xt) / (2y - x)
D.(2yt - xt) / (y - x)✓ Correct
Explanation
Let train length = L, speed = v. Then (L + x)/v = t and (L + y)/v = 2t. Subtracting: (y - x)/v = t, so v = (y-x)/t. From first equation: L = vt - x = (y-x) - x = y - 2x. Time for station (x+y): T = (L + x + y)/v = (y - 2x + x + y)/v = (2y - x)/v = (2y - x)t/(y - x) = (2yt - xt)/(y - x).
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