A train passes a pole in 10 seconds and a 120 m platform in 18 seconds. What is the length of the train (in metres)?
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
Answer
Correct Answer: 150 m
Explanation
Introduction / Context:Let L be the train length and v its speed. Passing a pole takes time to cover just L; passing a platform of length P takes time to cover L + P at the same speed v.
Given Data / Assumptions:
- Pole time = 10 s ⇒ L = v * 10.
- Platform = 120 m, platform time = 18 s ⇒ L + 120 = v * 18.
Concept / Approach:Eliminate v by dividing equations or substituting v = L/10 into the platform equation to solve for L directly.
Step-by-Step Solution:
L + 120 = (L/10) * 18 = 1.8L.120 = 1.8L − L = 0.8L ⇒ L = 120 / 0.8 = 150 m.Verification / Alternative check:Speed v = L/10 = 15 m/s; platform pass distance = 270 m; 270/15 = 18 s, consistent.
Why Other Options Are Wrong:130/180/240 m violate either the pole or platform timing when checked with the same v.
Common Pitfalls:Adding 120 m incorrectly or mixing seconds with metres without using speed.
Final Answer:150 m