All questions of Problems Based on Trains for SSC CGL Exam

Understanding the Problem
To determine how long it takes for a train to cross an 800-meter-long platform, we first need to find the speed of the train by analyzing its crossing times through the two tunnels.
Step 1: Calculate the Speed of the Train
- The length of the first tunnel is 200 meters, and the train crosses it in 40 seconds.
- The distance covered by the train when crossing the tunnel is the length of the tunnel plus the length of the train itself.
Let the length of the train be 'L' meters.
- Total distance for the first tunnel:
- Distance = Length of tunnel + Length of train = 200 + L meters
- Speed = Distance / Time
- Speed = (200 + L) / 40
- The length of the second tunnel is 500 meters, and the train crosses it in 55 seconds.
- Total distance for the second tunnel:
- Distance = 500 + L meters
- Speed = (500 + L) / 55
Setting the two speed equations equal gives us:
(200 + L) / 40 = (500 + L) / 55
Step 2: Solve for the Length of the Train
Cross-multiplying to solve for L:
55(200 + L) = 40(500 + L)
This simplifies to:
11000 + 55L = 20000 + 40L
Solving for L:
15L = 9000
L = 600 meters
Step 3: Calculate the Train's Speed
Using the value of L, we can find the speed:
- Speed = (200 + 600) / 40 = 800 / 40 = 20 meters/second
Step 4: Time to Cross the Platform
For an 800-meter platform, the total distance the train must cover is:
Total distance = Length of platform + Length of train = 800 + 600 = 1400 meters
Now, using the speed calculated:
Time = Distance / Speed = 1400 / 20 = 70 seconds
Conclusion
Thus, the train takes 70 seconds to cross an 800-meter-long platform, confirming that the correct answer is option 'C'.

Understanding the Problem
To determine how long it takes for a train to cross a pole after decreasing its speed by 75%, we need to analyze the information provided.
Initial Condition
- The train takes 75 seconds to cross a pole.
- Let the length of the train be L meters.
- Speed of the train can be calculated as:
Speed = Distance/Time
Therefore, Speed = L / 75 seconds.
New Speed Calculation
- If the speed is decreased by 75%, the new speed will be:
New Speed = Original Speed × (1 - 0.75)
New Speed = Original Speed × 0.25
New Speed = (L / 75) × 0.25 = L / 300 meters per second.
Time to Cross the Pole at New Speed
- To find the time taken to cross the pole at this new speed, we use the formula:
Time = Distance / Speed
Here, the distance is the length of the train (L), and the speed is now L / 300.
Time = L / (L / 300) = 300 seconds.
Conclusion
Thus, after reducing the speed by 75%, it will take the train 300 seconds to cross the same pole. Therefore, the correct answer is option 'D'.

Given data:
- Speed of Train A = 25 m/s
- Time taken by Train A to cross a pole = 20 seconds
- Time taken by Train A to cross Train B = 25 seconds

Calculating the length of the trains:
- Let the length of both trains be 'x' meters.

Calculating the speed of Train B:
- When Train A crosses Train B, the effective length to be covered is the sum of lengths of both trains.
- Time taken by Train A to cross Train B = 25 seconds
- Relative speed = Speed of Train A + Speed of Train B
- Distance = Sum of lengths of both trains
- Using the formula Distance = Speed * Time, we have:
x + x = (25 + Speed of Train B) * 25
2x = 25*25 + 25*Speed of Train B
2x = 625 + 25*Speed of Train B
25*Speed of Train B = 2x - 625
Speed of Train B = (2x - 625) / 25

Substitute the value of x:
- From the given data, we know that Train A crosses a pole in 20 seconds.
- So, length of Train A = 25 m/s * 20 seconds = 500 meters
- Substitute x = 500 meters in the equation for Speed of Train B:
Speed of Train B = (2*500 - 625) / 25
Speed of Train B = (1000 - 625) / 25
Speed of Train B = 375 / 25
Speed of Train B = 15 m/s
Therefore, the speed of Train B is 15 m/s. Hence, option 'A' is correct.