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Two Trains Crossing Each Other

CAT 2021 Slot 2 · Quantitative Ability · Medium · Speed & Time

This is a medium Quantitative Ability question from the CAT 2021 Slot 2 paper. It tests Speed & Time. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  1. A.

    184

  2. B.

    180

  3. C.

    190

  4. D.

    192

Answer

C

Explanation

Length of faster train L1=160 mL_1 = 160\text{ m}. Speed of faster train v1=16012=403 m/sv_1 = \frac{160}{12} = \frac{40}{3}\text{ m/s}. In km/hr: v1=403×185=48 km/hrv_1 = \frac{40}{3} \times \frac{18}{5} = 48\text{ km/hr}.

Speed of slower train v2=48−6=42 km/hrv_2 = 48 - 6 = 42\text{ km/hr}. In m/s: v2=42×518=353 m/sv_2 = 42 \times \frac{5}{18} = \frac{35}{3}\text{ m/s}.

Relative speed when moving in opposite directions: vrel=v1+v2=403+353=753=25 m/sv_{\text{rel}} = v_1 + v_2 = \frac{40}{3} + \frac{35}{3} = \frac{75}{3} = 25\text{ m/s}

Time taken to cross each other =14 seconds= 14\text{ seconds}. Total distance covered =L1+L2=vrel×14=25×14=350 m= L_1 + L_2 = v_{\text{rel}} \times 14 = 25 \times 14 = 350\text{ m}. 160+L2=350  ⟹  L2=190 m160 + L_2 = 350 \implies L_2 = 190\text{ m}.

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