Time, Speed and Distance Question 1 - CAT 2021
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:
Step-by-Step Explanation
Find the Speed of the Faster Train:
When a train crosses a stationary lamp post, it covers a distance equal to its own length.
Speed faster = 160 m/12 s = 40/3 m/s
Find the Speed of the Slower Train:
The slower train is 6 km/hr slower. Convert this speed gap into meters per second:
6 km/hr = 6 × 5/18 = 5/3 m/s
Speed slower = 40/3 − 5/3 = 35/3 m/s
Analyze the Trains Crossing Each Other:
When running in opposite directions, their relative speed is the sum of their individual speeds:
Relative Speed = 40/3 + 35/3 = 75/3 = 25 m/s
The total distance covered to cross each other completely is the sum of their lengths (160 + Lslower) over a time of 14 seconds:
160 + L slower = 25 × 14 = 350 m
L slower = 350 − 160 = 190 m
Correct Option: C
💡 FundaMakers Tip:
Keep your velocity values as fractions (40/3) instead of converting them to repeating decimals like 13.33 m/s. Fractional forms keep your arithmetic perfectly precise and allow values to cancel out cleanly when you calculate the final step.