2025 · Q50
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)?
Elementary MathematicsTime, Speed and Distance
- A(2yt + xt) / (y - x)
- B(yt + xt) / (y - x)
- C(3yt - xt) / (2y - x)
- D(2yt - xt) / (y - x)
Explanation
Let the train length be l and speed u: l + x = ut and l + y = 2ut. Subtracting gives y − x = ut, so u = (y−x)/t. The time for a station of length x + y is (l + x + y)/u = (ut + y)/u = t + yt/(y−x) = (2yt − xt)/(y−x), option (d).