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CAT 2021 Slot 1 — QA Question 6

TrainsEasy

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is

Answer & solution

  • A

    180

  • B

    184

  • 190

  • D

    192

Solution

Easy

Crossing a lamp post uses only the train's own length, so it gives the faster train's speed directly. The 66 km/hr gap gives the slower speed. Crossing each other in opposite directions uses the sum of lengths over the sum of speeds — solve for the unknown length.

Faster 160 m Slower L m → ←
1

Faster train's speed from the lamp post. Passing a post means covering its own length 160160 m in 1212 s.

f=16012=403 m/s\begin{aligned} &f=\frac{160}{12}=\frac{40}{3}\ \text{m/s} \end{aligned}
2

Slower train's speed. It is 66 km/hr slower; convert the gap to m/s with ×518\times\tfrac{5}{18}.

6 km/hr=6×518=53 m/s⇒ s=f−53=403−53=353 m/s\begin{aligned} &6\ \text{km/hr}=6\times\tfrac{5}{18}=\tfrac{5}{3}\ \text{m/s}\\ &\Rightarrow\ s=f-\tfrac{5}{3}=\tfrac{40}{3}-\tfrac{5}{3}=\tfrac{35}{3}\ \text{m/s} \end{aligned}
3

Crossing each other (opposite directions). Relative speed is the sum; combined length (160+L)(160+L) is covered in 1414 s.

f+s=403+353=753=25 m/s160+Lf+s=14⇒160+L=14×25=350⇒ L=350−160=190\begin{aligned} &f+s=\tfrac{40}{3}+\tfrac{35}{3}=\tfrac{75}{3}=25\ \text{m/s}\\ &\frac{160+L}{f+s}=14 \Rightarrow 160+L=14\times 25=350\\ &\Rightarrow\ L=350-160=190 \end{aligned}
Length of the other train=190 m(option (c))\text{Length of the other train}=190\ \text{m} \quad\text{(option (c))}
CAT 2021 Slot 1 QA Q6: Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faste — Solution | TheCATExam