Train Problems Quiz

Two mini trains of length 80 m and 120m, respectively, are moving on parallel tracks in opposite directions at 30 m/s and 20 m/s respectively. The time taken (in seconds) by both the mini trains to cross each other is :

• 8

• 4

• 10

• 6

Answer explanation

The total distance to be covered is 80 m + 120 m = 200 m. The relative speed is 30 m/s + 20 m/s = 50 m/s. Time taken = Distance / Speed = 200 m / 50 m/s = 4 seconds. Thus, the correct answer is 4.

Two trains are running in opposite directions on parallel tracks. If their speeds are 50 km/h and 58 km/h, find their relative speed.

• 20 m/s

• 40 m/s

• 30 m/s

• 50 m/s

Answer explanation

To find the relative speed of two trains moving in opposite directions, add their speeds: 50 km/h + 58 km/h = 108 km/h. Convert to m/s: 108 km/h × (1000 m/1 km) × (1 h/3600 s) = 30 m/s. Thus, the correct answer is 30 m/s.

Two trains start at the same time from two stations and proceed towards each other at 30 km/h and 35 km/h respectively. When they meet, it is found that one train has covered 30 km more than the other. Find the distance between the two stations.

• 400 km

• 380 km

• 390 km

• 410 km

Answer explanation

Let the distances covered by the trains be x and x+30. The time taken is the same, so x/30 = (x+30)/35. Solving gives x = 60 km. Total distance = x + (x + 30) = 60 + 90 = 390 km. Thus, the distance between the stations is 390 km.

A 250-metre long train running at a speed of 100 km/h crosses another train coming from the opposite direction at a speed of 62 km/h in 10 seconds. What is the length of the second train?

• 230 m

• 270 m

• 200 m

• 240 m

Answer explanation

The relative speed of the trains is 100 + 62 = 162 km/h, which is 45 m/s. In 10 seconds, they cover 450 m. Subtracting the 250 m of the first train, the second train is 200 m long.

Two trains of equal speed are running in opposite directions. If their lengths are 120 metres and 140 metres and they cross each other in 10 sec, then find the speed of each train.

• 13 m/s

• 10 m/s

• 16 m/s

• 14 m/s

Answer explanation

The total length of the trains is 120 + 140 = 260 metres. They cross each other in 10 seconds, so speed = distance/time = 260/10 = 26 m/s. Since both trains are moving towards each other, each train's speed is 26/2 = 13 m/s.

Two trains P and Q, having lengths of 300 m and 340 m respectively, are running towards each other. If P and Q are running at speeds of 35 m/s and 45 m/s, respectively, then how long will they take to cross each other?

• 8.5 sec

• 8 sec

• 9 sec

• 7 sec

Answer explanation

The relative speed of trains P and Q is 35 m/s + 45 m/s = 80 m/s. The total distance to be covered is 300 m + 340 m = 640 m. Time taken to cross each other = 640 m / 80 m/s = 8 sec. Thus, the correct answer is 8 sec.

Two trains from P and Q, respectively, at the same time and run towards each other at a speed of 40 km/h and 30 km/h, respectively. By the time they meet, the first train has covered 80 km more than the other train. Find the distance between P and Q.

• 660 km

• 240 km

• 560 km

• 630 km

Answer explanation

Let the distance covered by the second train be x km. Then, the first train covers x + 80 km. Using the relation: time = distance/speed, we have (x + 80)/40 = x/30. Solving gives x = 240 km, so total distance = 240 + 80 = 560 km.

Two trains starts at the same time from A and B proceed towards each other at speeds of 85 km per hour and 105 km per hour, respectively. When they meet, it is found that train from B has travelled 200 km more than the train from A. The distance between A and B.

• 1950 km

• 2000 km

• 1800 km

• 1900 km

Answer explanation

Let the distance from A to the meeting point be x km. Then, the distance from B is x + 200 km. Using the speeds, we have: x/85 = (x + 200)/105. Solving gives x = 900 km, so total distance = 900 + 1100 = 1900 km.

Two trains starting at the same time in opposite directions from two stations 200 km apart meet each other at a distance of 110 km from one of the stations. What is the ratio of their speed?

• 11 : 9

• 10 : 9

• 12 : 8

• 13 : 7

Answer explanation

The distance covered by the first train is 110 km, leaving 90 km for the second train. The ratio of their speeds is the inverse of the ratio of distances: 110:90 simplifies to 11:9, making the correct answer 11:9.

Two trains going in opposite directions, start at the same time from two stations that are 250 km apart. The trains meet each other at a distance of 130 km from one of the stations. Find the ratio of their speeds.

• 15 : 14

• 9 : 8

• 13 : 12

• 12 : 11

Answer explanation

The distance covered by the first train is 130 km, leaving 120 km for the second train. The ratio of their speeds is 130:120, which simplifies to 13:12. Thus, the correct answer is 13 : 12.