Question 1

A train crosses a platform of length 150 m in 18 seconds and crosses a pole in 12 seconds. What is the length of the train?

Accepted Answer

Step 1: Let the length of the train be L metres. When crossing a pole, the train travels its own length: L = Speed × 12. Step 2: When crossing the platform, the train travels L + 150: L + 150 = Speed × 18. Step 3: From equation 1, Speed = L/12. Substituting in equation 2: L + 150 = (L/12) × 18 = 1.5L. Step 4: 150 = 1.5L - L = 0.5L, so L = 300 m. Therefore, the length of the train is 300 m.

Question 2

Two trains of lengths 120 m and 180 m are moving in the same direction on parallel tracks. The faster train (120 m) travels at 90 km/h and the slower train (180 m) at 54 km/h. How long will it take for the faster train to completely overtake the slower train?

Accepted Answer

Step 1: Convert speeds to m/s: 90 km/h = 90 × (5/18) = 25 m/s; 54 km/h = 54 × (5/18) = 15 m/s. Step 2: Relative speed = 25 - 15 = 10 m/s (same direction). Step 3: Total distance to cover for complete overtaking = Length of both trains = 120 + 180 = 300 m. Step 4: Time = Distance ÷ Relative speed = 300 ÷ 10 = 30 seconds. Therefore, the faster train takes 30 seconds to completely overtake the slower train.

Question 3

A train starts from station A and travels towards station B at 72 km/h. After 3 hours, another train starts from station B towards station A at 90 km/h. If the distance between A and B is 540 km, at what distance from station A will the two trains meet?

Accepted Answer

Step 1: In 3 hours, the first train covers: 72 × 3 = 216 km from A. Step 2: Remaining distance between the two trains = 540 - 216 = 324 km. Step 3: Now both trains move towards each other with relative speed = 72 + 90 = 162 km/h. Step 4: Time to meet after the second train starts = 324 ÷ 162 = 2 hours. Step 5: Distance covered by the first train in these 2 hours = 72 × 2 = 144 km. Step 6: Total distance from A = 216 + 144 = 360 km. Therefore, the trains meet at 360 km from station A.

Question 4

Two trains start simultaneously from opposite ends of a 600 km track. Train X travels at 80 km/h and Train Y at 70 km/h. A bird starts flying from the front of Train X towards Train Y at 120 km/h. When the bird meets Train Y, it immediately turns back and flies towards Train X. This process continues until the trains meet. What is the total distance covered by the bird?

Accepted Answer

Step 1: The key insight is that the bird keeps flying until the two trains meet, regardless of how many times it changes direction. Step 2: Time taken for the trains to meet = Total distance ÷ Relative speed = 600 ÷ (80 + 70) = 600 ÷ 150 = 4 hours. Step 3: The bird flies continuously for these 4 hours at 120 km/h. Step 4: Total distance covered by the bird = Speed of bird × Time = 120 × 4 = 480 km. Therefore, the bird covers 480 km in total.

SSC GD Constable Time, Speed & Distance Questions

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