A passenger train of length 60 m travels at a speed of $80 \mathrm{~km} / \mathrm{hr}$. Another freight train of length 120 m travels at a speed of $30 \mathrm{~km} / \mathrm{hr}$. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is:

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Kinematics

A passenger train of length 60 m travels at a speed of

80 km / hr

. Another freight train of length 120 m travels at a speed of

30 km / hr

. The ratio of times taken by the passenger train to completely cross the freight train when:
(i) they are moving in the same direction, and
(ii) in the opposite directions is:

(A) $\frac{11}{5}$ ✓ Correct
(B) $\frac{5}{2}$
(C) $\frac{3}{2}$
(D) $\frac{25}{11}$

Answer: (A)

Solution

To completely cross the freight train the passenger train must cover the sum of the two lengths,

60 + 120 = 180 m

, in both cases; the distance is the same, so the times go purely as the inverse of the relative speed. Moving in the same direction the relative speed is

80 - 30 = 50 km/h

, while in opposite directions it is

80 + 30 = 110 km/h

. The ratio of the times is therefore the inverse ratio of these speeds,

\frac{t _{same}}{t _{opp}} = \frac{110}{50} = \frac{11}{5}

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Kinematics

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