Train Crossing a Pole: Formula, Rules and Solved Questions

Train Crossing a Pole problems calculate the time taken by a train to pass a fixed point. Since a pole has negligible length, the train covers only its own length. The basic relation is distance = speed × time, so train length, speed and crossing time can be calculated when any two values are known.

On this page

What Happens When a Train Crosses a Pole?

When a train crosses a pole, it covers a distance equal to its own length. Therefore, time taken = train length ÷ train speed.

A pole is treated as a fixed point with negligible length. If the train length is L metres and its speed is v metres per second, the front of the train travels L metres before the rear leaves the pole. Thus, t = L/v. For example, a 150 m train moving at 15 m/s crosses a pole in 150 ÷ 15 = 10 seconds.

Train Crossing a Pole Formula & Tricks

Important Formulas

Time to cross a pole
t = L/v

Time t equals train length L divided by speed v. Use L in metres and v in metres per second.

Train length
L = v × t

Train length is the product of speed and the time taken to cross the pole.

Train speed
v = L/t

Speed is obtained by dividing train length by crossing time.

Speed conversion
1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h

Convert km/h to m/s before using the pole-crossing formula when length is given in metres.

Quick Tricks

Use only the train length

For a pole, signal, person or tree, the object is treated as a point. Do not add another length to the train length.

Example: A 180 m train crossing a pole covers 180 m, not 181 m or any other distance.
Convert speed before calculation

If length is in metres and time is in seconds, convert speed from km/h to m/s using multiplication by 5/18.

Example: 54 km/h = 54 × 5/18 = 15 m/s. A 120 m train then takes 120/15 = 8 seconds.
Use proportionality for equal trains

At the same speed, crossing time is directly proportional to train length. At the same train length, time is inversely proportional to speed.

Example: If a train takes 12 seconds at 20 m/s, it takes 8 seconds at 30 m/s for the same length because time changes in the ratio 20:30.

Train Crossing a Pole Concepts

Calculating Time from Train Length and Speed

The time taken to cross a pole is found by dividing the train length by its speed in metres per second.

Use t = L/v. First convert the speed into m/s if it is given in km/h. The answer is obtained in seconds when length is in metres and speed is in m/s.

Example: For a 240 m train moving at 72 km/h, speed = 72 × 5/18 = 20 m/s. Time = 240/20 = 12 seconds.

Finding Train Length

Train length equals speed multiplied by the time taken to cross the pole.

Use L = v × t. The speed and time units must match. If speed is in m/s and time is in seconds, the calculated length is in metres.

Example: A train moving at 18 m/s crosses a pole in 14 seconds. Its length = 18 × 14 = 252 m.

Finding Speed from Crossing Time

Train speed equals train length divided by the time taken to cross the pole.

Use v = L/t. This gives speed in m/s when length is in metres and time is in seconds. Convert the result to km/h by multiplying by 18/5.

Example: A 300 m train crosses a pole in 15 seconds. Speed = 300/15 = 20 m/s = 20 × 18/5 = 72 km/h.

Effect of Changing Speed or Length

For a fixed train length, crossing time decreases when speed increases; for a fixed speed, crossing time increases with train length.

Since t = L/v, time is directly proportional to L and inversely proportional to v. If speed becomes twice as large, time becomes half for the same train. If length becomes three times as large at the same speed, time becomes three times as large.

Example: A 200 m train takes 10 seconds at 20 m/s. At 40 m/s, it takes 200/40 = 5 seconds.

Train Crossing a Pole Video Lessons

Watch short topic-wise lessons for quick revision.

11 Lessons
Lesson 1 of 11 Quick Revision

Trains Crossing a Pole or Person

Learn how to calculate the time, speed, or length of a train when it crosses a pole or a person using the appropriate distance and speed relationships.

Continue with more lessons and practice in PrepShots.Watch More in App - Start ₹1 Trial →
More Train Crossing a Pole Lessons Scroll to explore →

Practice Train Crossing a Pole Questions

Practise published questions related to this topic.

1An article is marked at Rs. 400. If sold at a 10% discount, what is the selling price ?→ 2Which of the following number is divisible by both 4 and 9?→ 3A trader sets a price 40% above cost and offers a 20% discount. What is the profit percentage?→ 4What is the Highest Common Factor of 5/12, 15/20 and 25/30?→ 5The profit earned on selling an article for Rs. 2000 is 19 times of the loss incurred on selling the same article for Rs. 1200. What is the profit percentage on this article at the selling price of Rs. 2000?→ 6What will be the number of zeros at the end of the square of the following numbers? (i) 70 (ii) 500 Choose the correct option:→ 7If an item marked at ₹1,675 is sold for ₹1,273, then what is the discount percentage?→ 8The Highest Common Factor of the two numbers is 10. Which of the following can be the Least Common Multiple of the two numbers?→ 9Evaluate: 3⁵ × 7⁵ ÷ 21³→ 10A trader bought goods at ₹600 and made a profit of ₹120 .Find the profit percentage.→

Train Crossing a Pole Quick Quiz

Attempt 5 questions and check your score instantly.

Quick Revision Notes

Train Crossing a Pole: Quick Revision

Use these direct rules and formulas to solve pole-crossing questions.

  • A pole has negligible length, so distance covered equals the train's length.
  • Time = train length ÷ speed, or t = L/v.
  • Train length = speed × time, or L = v × t.
  • Speed = train length ÷ time, or v = L/t.
  • Use metres and seconds together, or kilometres and hours together.
  • Convert km/h to m/s by multiplying by 5/18.
  • Convert m/s to km/h by multiplying by 18/5.
  • For the same train, higher speed means less crossing time.

Train Crossing a Pole FAQs

What is the train crossing a pole formula?

The formula is t = L/v, where t is time, L is train length and v is speed. Use length in metres and speed in metres per second to obtain time in seconds.

How far does a train travel while crossing a pole?

It travels a distance equal to its own length because the pole is treated as a point. A 250 m train therefore covers 250 m while crossing a pole.

A 180 m train moves at 54 km/h. How long does it take to cross a pole?

54 km/h = 54 × 5/18 = 15 m/s. Time = 180/15 = 12 seconds.

A train crosses a pole in 16 seconds at 25 m/s. What is its length?

Length = speed × time = 25 × 16 = 400 m.

A 225 m train crosses a pole in 9 seconds. What is its speed in km/h?

Speed = 225/9 = 25 m/s. In km/h, 25 × 18/5 = 90 km/h.

Should the pole's length be added to the train length?

No. A pole is considered to have negligible length, so the required distance is only the train's length.

Continue learning Train Crossing a Pole on PrepShots

Continue on PrepShots