Train Crossing a Platform: Formula, Method and Examples

Train Crossing a Platform questions involve finding the time a train takes to cover its own length plus the platform length. The basic distance is train length + platform length, and time is obtained by dividing this distance by the train’s speed. Speed units must be made consistent before calculation.

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What Is Train Crossing a Platform?

A train crosses a platform when the complete train covers the combined length of the train and the platform. Therefore, the distance travelled is train length + platform length.

If the train length is L metres and the platform length is P metres, the required distance is L + P metres. For speed v metres per second, time t is calculated by t = (L + P) / v seconds. If speed is given in kilometres per hour, convert it using v m/s = v km/h × 5/18. For example, a 120 m train crossing a 180 m platform covers 300 m in total.

Train Crossing a Platform Formula & Tricks

Important Formulas

Distance covered while crossing a platform
Distance = Train length + Platform length = L + P

The train must completely leave the platform, so its front covers both its own length and the platform length.

Time taken to cross a platform
Time = (L + P) / v

Use this formula when L and P are in metres and v is in metres per second.

Speed conversion
Speed in m/s = Speed in km/h × 5/18

Multiply a speed in kilometres per hour by 5/18 before using lengths in metres.

Platform length
P = (v × t) − L

When time and speed are known, subtract the train length from the total distance travelled.

Quick Tricks

Add lengths before dividing

For a stationary platform, first add the train length and platform length. Dividing only the platform length gives the time for the train’s front to reach the end, not the time for the whole train to cross.

Example: A 150 m train crossing a 250 m platform travels 400 m, not 250 m.
Use 18/5 for km/h to m/s mentally

Dividing a speed in km/h by 3.6 is the same as multiplying it by 5/18. This prevents unit mismatch with metre-based lengths.

Example: 72 km/h = 72 × 5/18 = 20 m/s.
Check the answer using distance = speed × time

After finding the time, multiply speed by time. The result must equal train length + platform length.

Example: At 20 m/s for 20 seconds, the distance is 400 m, matching a 150 m train plus a 250 m platform.

Train Crossing a Platform Concepts

Distance Required to Cross a Platform

The distance required is the sum of the train length and the platform length.

Let the train length be L and the platform length be P. When the train’s front reaches the far end of the platform, the rear is still L metres behind it. Hence, the complete train crosses after covering L + P metres.

Example: For a 180 m train and a 320 m platform, distance = 180 + 320 = 500 m.

Converting Speed Before Calculation

Lengths in metres require speed in metres per second for direct use in the time formula.

Convert v km/h to v × 5/18 m/s. Alternatively, if the answer is required in seconds and distance is in metres, use time = distance × 18 / (speed in km/h × 5).

Example: A speed of 54 km/h is 54 × 5/18 = 15 m/s.

Finding Time to Cross a Platform

Time is found by dividing the combined length by the train’s speed in metres per second.

Use t = (L + P) / v. For a 200 m train crossing a 300 m platform at 25 m/s, t = (200 + 300)/25 = 20 seconds.

Example: The train covers 500 m at 25 m/s, so it takes 20 seconds.

Finding Train or Platform Length

An unknown length can be obtained by rearranging the distance formula.

If platform length is unknown, P = vt − L. If train length is unknown, L = vt − P. Here, v must be in m/s when t is in seconds and lengths are in metres.

Example: A train moving at 20 m/s crosses a platform in 30 seconds. If the train is 250 m long, platform length = 20 × 30 − 250 = 350 m.

Train Crossing a Platform Video Lessons

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Practice Train Crossing a Platform Questions

Practise published questions related to this topic.

195P9 is divisible by 3. What is the value of P?→ 2A refrigerator is marked at Rs. 9,600. A shopkeeper offers successive discounts of 12% and 25%. If he still earns a profit of 20%, find the cost price of the refrigerator.→ 3After allowing a discount of 9% on the marked price of an article, it is sold for ₹53,053. Find its marked price (in ₹).→ 4A trader buys an article, spends ₹50 on its repair, and sells it for ₹600, making a 25% profit. What was the original purchase price?→ 5The 7-digit number 77A444B is divisible by 24. What is the maximum value of (A + B)?→ 6Simplify: ((2x²y⁻¹)³)/((4xy)⁴) × ((4x⁻³y⁴)³)/((2x²y)³)→ 7The marked price of a cooker is the same at four shops I, II, III and IV. Shop I allows two successive discounts of 87% and 37%, shop II allows successive discounts of 81% and 37%, shop III allows successive discounts of 57% and 54% and shop IV allows successive discounts of 91%, 25%, and 59% on the marked price of the cooker. Which shop is selling the cooker at the lowest price?→ 8An article is sold for 30 percent loss. The value of discount given is equal to the (7/10) of the selling price. Cost price of the article is what percent of its marked price?→ 9If x = √(1671 + √(93 + √49)) , then what is the value of x?→ 10Find the value of m which satisfies (26/7)⁵ × (7/26)¹¹ × (26/7)¹⁹ = (7/26)^(9m+17)→

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Quick Revision Notes

Train Crossing a Platform: Quick Revision

Use these direct rules and formulas while solving numerical questions.

  • Required distance = train length + platform length.
  • Time = (train length + platform length) / speed.
  • Convert km/h to m/s by multiplying by 5/18.
  • Use metres and seconds together, or kilometres and hours together.
  • For an unknown platform length, use P = vt − L.
  • The train crosses completely only when its rear end reaches the far end of the platform.

Train Crossing a Platform FAQs

What is the train platform formula?

Time = (Train length + Platform length) / Train speed. Use speed in m/s when both lengths are in metres.

A 100 m train crosses a 200 m platform at 15 m/s. What time does it take?

Total distance = 100 + 200 = 300 m. Time = 300/15 = 20 seconds.

Why is the train length added to the platform length?

The front of the train must travel the platform length, and the rear must also cover the train’s own length before the train has completely crossed.

How do you solve a platform question when speed is 72 km/h?

Convert the speed first: 72 × 5/18 = 20 m/s. Then use time = (train length + platform length)/20.

A 250 m train crosses a 350 m platform in 30 seconds. What is its speed?

Distance = 250 + 350 = 600 m. Speed = 600/30 = 20 m/s = 72 km/h.

How is crossing a platform different from crossing a pole?

For a pole, the train covers only its own length, so time = train length/speed. For a platform, it covers train length + platform length.

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