13. Trains and platforms
Free study material · concepts, shortcuts & solved questions
Time to cross a pole = train length ÷ speed. Time to cross a platform = (train length + platform length) ÷ speed. For two trains, use relative speed and add lengths for opposite direction; subtract lengths are not used—the physical distance to clear is the sum.
Method before formula Convert every length to metres and speed to m/s. Draw the starting and finishing positions if direction or platform wording is confusing. |
Formula and decision table
Case | Distance |
Pole/person | Train length |
Platform | Train + platform |
Two trains opposite | Length₁+length₂; speed₁+speed₂ |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
A 180 m train at 54 km/h crosses a pole in: | 54 km/h=15 m/s; 180/15=12 s. | B. 12 s |
A 180 m train crosses a 120 m platform at 15 m/s. Time: | Distance=300 m; time=20 s. | C. 20 s |
Same-direction relative speed is: | Subtract the lower speed from the higher. | B. u−v |
What an examiner is testing
The options around Trains and platforms usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: A 180 m train at 54 km/h crosses a pole in: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 12 s, because 54 km/h=15 m/s; 180/15=12 s.
Example 2: A 180 m train crosses a 120 m platform at 15 m/s. Time: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 20 s, because Distance=300 m; time=20 s.
Example 3: Same-direction relative speed is: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is u−v, because Subtract the lower speed from the higher.
Chapter practice
1. A 180 m train at 54 km/h crosses a pole in:
(A) 10 s (B) 12 s (C) 15 s (D) 18 s
Answer: B. 12 s | Explanation: 54 km/h=15 m/s; 180/15=12 s.
2. A 180 m train crosses a 120 m platform at 15 m/s. Time:
(A) 12 s (B) 15 s (C) 20 s (D) 24 s
Answer: C. 20 s | Explanation: Distance=300 m; time=20 s.
3. Same-direction relative speed is:
(A) u+v (B) u−v (C) uv (D) u/v
Answer: B. u−v | Explanation: Subtract the lower speed from the higher.
SSC CGL speed and trap clinic
For Trains and platforms, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Trains and platforms? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Trains and platforms question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |