Theory & Concepts
SSC CGL Train Problems Questions, Formulas & Tricks
Prepare Train Problems for SSC CGL with formulas, short tricks, solved examples, practice questions, PYQs, and free PDF notes for faster exam preparation.
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22 min readDifficulty: Intermediate
Train problems are a prime candidate for the Ssc cgl quantitative section. Unlike traditional speed-distance problems, trains introduce the concept of "Object Length" and "Relative Motion" in parallel tracks.
The secret to solving these in under 30 seconds is knowing when to add the lengths and when to subtract the speeds. This guide provides the high-fidelity formulas and shortcuts required for Tier-2 accuracy.
Learning path
- Poles vs Platforms crossing rules
- Relative Speed logic (Opposite/Same)
- Unit conversion shortcuts (km/h m/s)
- 10 master solved problems
- Overtaking logic for CGL
1. Direct crossing formulas
Distance covered (d)
A: Crossing a Point Object (Pole, Man):
B: Crossing a Static Object (Platform, Bridge):
2. Relative speed rules
Same Direction:
Subtract Speeds
Opposite Direction:
Add Speeds
3. 10 Solved examples
Question 01Standard pattern
A train 150m long is running at 54 km/hr. How much time will it take to cross a telephone pole?
10 sec
12 sec
15 sec
8 sec
Correct answer: a) 10 sec
Solution
First, convert speed to m/s: \( 54 \times \frac{5}{18} = 15 \text{ m/sec} \).
Distance = Length of train = \( 150 \text{ m} \).
Time = \( 150 / 15 = 10 \text{ seconds} \).
Question 02Standard pattern
A train 200m long passes a 300m long platform in 25 seconds. What is the speed of the train in km/hr?
72 km/hr
60 km/hr
80 km/hr
64 km/hr
Correct answer: a) 72 km/hr
Solution
Total distance = \( 200 + 300 = 500 \text{ m} \).
Speed (m/s) = \( 500 / 25 = 20 \text{ m/s} \).
Speed (km/hr) = \( 20 \times \frac{18}{5} = 72 \text{ km/hr} \).
Question 03Standard pattern
Two trains of length 150m and 170m are running in opposite directions at speeds of 40 km/hr and 32 km/hr. In what time will they cross each other?
16 sec
15 sec
18 sec
20 sec
Correct answer: a) 16 sec
Solution
Total length = \( 150 + 170 = 320 \text{ m} \).
Relative speed = \( 40 + 32 = 72 \text{ km/hr} \).
Convert speed to m/s: \( 72 \times \frac{5}{18} = 20 \text{ m/s} \).
Time = \( 320 / 20 = 16 \text{ seconds} \).
Question 04Standard pattern
A train 110m long passes a man running at 6 km/hr in the same direction in 6 seconds. What is the speed of the train?
72 km/hr
100 km/hr
68 km/hr
60 km/hr
Correct answer: a) 72 km/hr
Solution
Relative speed in m/s = \( 110/6 \text{ m/s} \).
Relative speed in km/hr = \( \frac{110}{6} \times \frac{18}{5} = 66 \text{ km/hr} \).
Since same direction, Rel Speed = \( V_t - V_m \).
\( 66 = V_t - 6 \implies V_t = 72 \text{ km/hr} \).
Question 05Standard pattern
A train overtakes two persons walking at 2 km/hr and 4 km/hr in the same direction and passes them in 9 and 10 seconds. Find length of train.
50m
100m
60m
75m
Correct answer: a) 50m
Solution
Let speed be \( v \). \( L = (v-2) \times 9 = (v-4) \times 10 \).
Calculation: \( 9v - 18 = 10v - 40 \implies v = 22 \text{ km/hr} \).
Length = \( (22 - 2) \times \frac{5}{18} \times 9 = 50 \text{ m} \).
Question 06Standard pattern
A train passes a station platform in 36 seconds and a man on platform in 20 seconds. Speed is 54 km/hr. Length of platform?
240m
300m
270m
200m
Correct answer: a) 240m
Solution
Speed = \( 54 \times 5/18 = 15 \text{ m/s} \).
Length of train = \( 15 \times 20 = 300 \text{ m} \).
Total length (Train + Plat) = \( 15 \times 36 = 540 \text{ m} \).
Bridge/Platform length = \( 540 - 300 = 240 \text{ m} \).
Question 07Standard pattern
Two trains of equal length cross a pole in 20 and 30 seconds respectively. In same direction, how long to cross each other?
120 sec
100 sec
60 sec
90 sec
Correct answer: a) 120 sec
Solution
Let length of each train be \( 60 \text{ m} \) (LCM of 20, 30).
Speeds: \( 3 \text{ m/s} \) and \( 2 \text{ m/s} \).
Relative Speed (Same) = \( 3 - 2 = 1 \text{ m/s} \).
Time = \( (60+60) / 1 = 120 \text{ seconds} \).
Question 08Standard pattern
Two stations A and B are 110 km apart. Train from A starts at 7 am at 20 kmph. Train from B starts at 8 am at 25 kmph towards A. Meeting time?
10 am
11 am
9 am
12 noon
Correct answer: a) 10 am
Solution
At 8 am, distance between them = \( 110 - 20 = 90 \text{ km} \).
Relative speed = \( 20 + 25 = 45 \text{ kmph} \).
Time = \( 90/45 = 2 \text{ hours} \) after 8 am.
Result = 10 am.
Question 09Standard pattern
Length of train is 240 m. In 24 sec it crosses pole. How long to cross 650 m platform?
89 sec
80 sec
100 sec
95 sec
Correct answer: a) 89 sec
Solution
Speed = \( 240 / 24 = 10 \text{ m/s} \).
Total dist = \( 240 + 650 = 890 \text{ m} \).
Time = \( 890 / 10 = 89 \text{ seconds} \).
Question 010Standard pattern
Two trains of length 100m and 80m are on parallel tracks. In same direction cross in 18s, opposite in 9s. Find speeds.
15 & 5 m/s
10 & 5 m/s
12 & 8 m/s
20 & 10 m/s
Correct answer: a) 15 & 5 m/s
Solution
Total length = 180 m.
\( V_1 - V_2 = 180 / 18 = 10 \).
\( V_1 + V_2 = 180 / 9 = 20 \).
Solving: \( 2V_1 = 30 \implies V_1 = 15 \), \( V_2 = 5 \).
4. Strategy errors to avoid
Error 01Unit neglect: Forgetting to convert km/hr to m/s before adding train lengths.
Error 02Static distance: Forgetting to add the platform length to the train length for crossing time.
Error 03Same direction trap: Adding speeds when trains are moving in the same direction (should subtract).
Error 04Meeting time error: Not accounting for the different start times of two trains.
