Problems on Trains questions with answers and concepts

Learn problems on trains with concept notes and worked examples, then practise focused questions with explained answers. Build accuracy for placement and competitive aptitude tests before trying timed mode.

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Problems on trains are a classic topic in aptitude tests that involve calculating time, speed, and distance in scenarios involving trains crossing various objects like poles, platforms, bridges, and other trains. These problems test your understanding of relative speed and distance concepts in practical situations.

Key formulas and rules

10 rules

Basic relationship: $Speed = \frac{Distance}{Time}$ , $Time = \frac{Distance}{Speed}$ , $Distance = Speed \times Time$

Unit conversion: $1 km/h = \frac{5}{18} m/s$ and $1 m/s = \frac{18}{5} km/h$

Crossing a point object (pole/person): $T = \frac{L _{train}}{S _{train}}$

Crossing an extended object (platform/bridge/tunnel): $T = \frac{L _{train} + L _{platform}}{S _{train}}$

Relative speed in same direction: $S_{rel} = ∣ S_{1} - S_{2} ∣$

Relative speed in opposite direction: $S_{rel} = S_{1} + S_{2}$

Two trains crossing (opposite direction): $T = \frac{L _{1} + L _{2}}{S _{1} + S _{2}}$

Two trains crossing (same direction): $T = \frac{L _{1} + L _{2}}{∣ S _{1} - S _{2} ∣}$

Train crossing a moving person (same direction): $T = \frac{L _{train}}{S _{train} - S _{person}}$

Train crossing a moving person (opposite direction): $T = \frac{L _{train}}{S _{train} + S _{person}}$

Key concepts

Crossing a Stationary Object (Pole/Signal Post)

When a train crosses a stationary object like a pole or signal post, the distance covered equals the length of the train itself. The object has negligible length, so time taken = Length of train / Speed of train. This is the simplest case of train problems.

Crossing a Platform or Bridge

When a train crosses a platform or bridge, the total distance to be covered is the sum of the train's length and the platform/bridge length. The time taken = (Length of train + Length of platform) / Speed of train. This is because the train is considered to have completely crossed only when its rear end clears the far end of the platform.

Two Trains Moving in Opposite Directions

When two trains move towards each other in opposite directions, they approach each other with a relative speed equal to the sum of their individual speeds (S + S ). The total distance to cover for complete crossing is the sum of both trains' lengths. Time = (L + L ) / (S + S ).

Two Trains Moving in Same Direction

When two trains move in the same direction, the relative speed is the difference of their speeds (faster - slower). The faster train overtakes the slower one. Time to completely pass = (L + L ) / |S - S |. This scenario requires the faster train to cover both trains' lengths at the relative speed.

A Train Crossing a Moving Object/Person

When a train crosses a moving object (person walking or another vehicle), calculate relative speed based on direction. Same direction: Relative speed = Train speed - Object speed. Opposite direction: Relative speed = Train speed + Object speed. Then use Time = Train length / Relative speed.

Unit Conversion

Train problems often require converting between km/hr and m/s. To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5. Always ensure consistent units before calculating - if lengths are in meters and times in seconds, convert speeds to m/s.

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Worked examples

Example 1

A train 150 metres long is travelling at 72 km/h. How long will it take to pass a stationary telegraph pole?

Solution

Step 1: Convert speed to m/s.

s = 72 \times \frac{5}{18} m/s = 20 m/s

Step 2: Distance to cross a point object equals the length of the train.

T = \frac{L _{train}}{s} = \frac{150 m}{20 m/s} = 7.5 seconds

Answer: 7.5 seconds.

Example 2

A train 180 metres long running at 90 km/h crosses a platform 220 metres long. Find the time taken to cross the platform completely.

Solution

Step 1: Convert speed to m/s.

s = 90 \times \frac{5}{18} m/s = 25 m/s

Step 2: Total distance equals train length plus platform length.

D = L_{train} + L_{platform} = 180 + 220 = 400 metres

Step 3: Calculate crossing time.

T = \frac{D}{s} = \frac{400}{25} = 16 seconds

Answer: 16 seconds.

Example 3

Two trains with lengths 120 m and 130 m run on parallel tracks in opposite directions at 65 km/h and 43 km/h respectively. How long do they take to cross each other from the moment they meet?

Solution

Step 1: Calculate total relative speed for opposite directions.

s_{rel} = s_{1} + s_{2} = 65 + 43 = 108 km/h

s_{rel} = 108 \times \frac{5}{18} m/s = 6 \times 5 = 30 m/s

Step 2: Total distance to clear both bodies.

D = L_{1} + L_{2} = 120 + 130 = 250 metres

Step 3: Compute crossing time.

T = \frac{250}{30} = \frac{25}{3} = 8 \frac{1}{3} seconds \approx 8.33 seconds

Answer: $8 \frac{1}{3}$ seconds (or approximately 8.33 seconds).

Example 4

Two trains of equal length 100 metres each run in opposite directions and pass each other in 7.2 seconds. If the speed of the first train is 60 km/h, what is the speed of the second train?

Solution

Step 1: Total distance covered during crossing.

D = 100 + 100 = 200 metres

Step 2: Determine relative speed in m/s.

s_{rel} = \frac{D}{T} = \frac{200 m}{7.2 s} = \frac{2 , 000}{72} = \frac{250}{9} m/s

Step 3: Convert relative speed to km/h.

s_{rel} = \frac{250}{9} \times \frac{18}{5} = 50 \times 2 = 100 km/h

Step 4: Solve for $s_{2}$ .

s_{1} + s_{2} = 100 ⟹ 60 + s_{2} = 100 ⟹ s_{2} = 40 km/h

Answer: 40 km/h.

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

A train 300 m long is running at a speed of 54 km/hr. In how many seconds will it cross a pole?

10 seconds
15 seconds
20 seconds
25 seconds

Answer: C. 20 seconds

Explanation

Step 1: Speed = 54 $k m / h r = 54$ x $(5/18) = 15$ m/sec
Step 2: Time = Distance/Speed = 300/15 = 20 seconds
Answer: 20 seconds

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

A train running at a speed of 72 km/hr crosses a pole in 10 seconds. The length of the train is:

100 m
150 m
200 m
250 m

Answer: C. 200 m

Explanation

Step 1: Speed = 72 $k m / h r = 72$ x $(5/18) = 20$ m/sec
Step 2: Distance = Speed x Time = 20 x $10 = 200$ m
Answer: 200 m

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

A train 100 m long crosses a platform of 200 m in 20 seconds. The speed of the train is:

36 km/hr
45 km/hr
54 km/hr
60 km/hr

Answer: C. 54 km/hr

Explanation

Step 1: Total distance = Length of train + Length of platform = 100 + 200 = 300 m
Step 2: Speed = Distance/Time = 300/20 = 15 m/sec
Step 3: Convert to $k m / h r = 15$ x $(18/5) = 54$ km/hr
Answer: 54 km/hr

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Always convert speed to m/s when lengths are given in meters - multiply km/hr by 5/18.
Remember: When crossing a pole, only the train's length matters. When crossing a platform/bridge, add both lengths.
For two trains: Add lengths, then use relative speed based on direction (add speeds for opposite, subtract for same).
A train 'crossing' or 'passing' another train means from the moment the fronts meet until the rears separate.
If a problem involves a train crossing a moving person or object, calculate relative speed first, then apply the same formulas.
Draw a simple diagram if confused - it helps visualize what distance needs to be covered.

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