Numerical: Trains, Boats & Streams MCQ — 14 Practice Questions with Answers

Explanation

For a boat, downstream speed = still-water speed + stream speed = 10 + 2 = 12 km/h. Upstream speed = still-water speed − stream speed = 10 − 2 = 8 km/h. Time = distance ÷ speed. Therefore, time for 48 km downstream = 48 ÷ 12 = 4 hours, and time for 24 km upstream = 24 ÷ 8 = 3 hours. These four values match option A.

Explanation

To pass a standing man, the train has to cover only its own length. Convert the speed into m/s: 54 km/h = 54 × 5/18 = 15 m/s. Distance to be covered = 180 m. Time = distance ÷ speed = 180 ÷ 15 = 12 seconds. No platform length is added because the man is a point object. Therefore, the train will pass him in 12 seconds.

Explanation

For trains moving in the same direction, relative speed is the difference of their speeds. Here, relative speed = 54 − 36 = 18 km/h = 18 × 5/18 = 5 m/s. While one train overtakes the other, the distance covered is the sum of their lengths: 150 + 250 = 400 m. Time = distance ÷ relative speed = 400 ÷ 5 = 80 seconds. Therefore, the statement saying that the overtaking time is 40 seconds is incorrect.

Explanation

When a train crosses a platform, it covers the sum of the train length and the platform length. Total distance = 120 + 180 = 300 m. Time = 20 seconds. Speed = distance ÷ time = 300 ÷ 20 = 15 m/s. Convert this into km/h: 15 × 18/5 = 54 km/h. Hence the correct statement is that the speed of the train is 54 km/h.

Explanation

Downstream speed equals the speed of the boat in still water plus the speed of the stream. So downstream speed = 12 + 3 = 15 km/h. The distance to be covered is 30 km. Time = distance ÷ speed = 30 ÷ 15 = 2 hours. The stream helps the boat in the downstream direction, so its speed must be added, not subtracted. Therefore, the required time is 2 hours.