Quantitative Apptitude - Problems On Train Online Test 6

1. With a speed of 60 kmph a train crosses a pole in 30 seconds. the length of the train is?

800 m

500 m

1000 m

360 m

The length of the train can be calculated using the formula: Length = Speed × Time. In this case, the speed of the train is given as 60 kmph, which needs to be converted to meters per second. Since 1 km = 1000 m and 1 hour = 3600 seconds, the speed in meters per second is 60 × 1000 / 3600 = 16.67 m/s. The time taken to cross the pole is given as 30 seconds. Substituting these values into the formula, we get Length = 16.67 × 30 = 500 m. Therefore, the length of the train is 500 m.

Explanation

The length of the train can be calculated using the formula: Length = Speed × Time. In this case, the speed of the train is given as 60 kmph, which needs to be converted to meters per second. Since 1 km = 1000 m and 1 hour = 3600 seconds, the speed in meters per second is 60 × 1000 / 3600 = 16.67 m/s. The time taken to cross the pole is given as 30 seconds. Substituting these values into the formula, we get Length = 16.67 × 30 = 500 m. Therefore, the length of the train is 500 m.

2. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

230 m

270 m

265 m

290 m

When two trains are moving in opposite directions, their relative speed is the sum of their individual speeds. In this case, the first train is moving at 120 kmph and the second train is moving at 80 kmph. Therefore, their relative speed is 120 kmph + 80 kmph = 200 kmph.

To find the length of the other train, we need to convert the relative speed from kmph to m/s. 200 kmph is equal to (200 * 1000) / (60 * 60) = 55.56 m/s.

We also know that the time taken to cross the other train is 9 seconds.

Using the formula distance = speed * time, we can calculate the distance traveled by the first train in 9 seconds.

Distance = 55.56 m/s * 9 seconds = 500.04 meters.

Since the length of the first train is given as 270 meters, the length of the other train can be calculated by subtracting the length of the first train from the total distance traveled.

Length of the other train = 500.04 meters - 270 meters = 230 meters.

Therefore, the length of the other train is 230 meters.

Explanation

When two trains are moving in opposite directions, their relative speed is the sum of their individual speeds. In this case, the first train is moving at 120 kmph and the second train is moving at 80 kmph. Therefore, their relative speed is 120 kmph + 80 kmph = 200 kmph.

To find the length of the other train, we need to convert the relative speed from kmph to m/s. 200 kmph is equal to (200 * 1000) / (60 * 60) = 55.56 m/s.

We also know that the time taken to cross the other train is 9 seconds.

Using the formula distance = speed * time, we can calculate the distance traveled by the first train in 9 seconds.

Distance = 55.56 m/s * 9 seconds = 500.04 meters.

Since the length of the first train is given as 270 meters, the length of the other train can be calculated by subtracting the length of the first train from the total distance traveled.

Length of the other train = 500.04 meters - 270 meters = 230 meters.

Therefore, the length of the other train is 230 meters.

3. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

15 s

36 s

45 s

85 s

The train is moving at a speed of 45 kmph and the jogger is running at a speed of 9 kmph. Since they are moving in the same direction, the relative speed between them is the difference of their speeds, which is 36 kmph.

To find the time it takes for the train to pass the jogger, we need to calculate the distance between them. The jogger is 240 meters ahead of the train, and the train is 120 meters long. So, the total distance is 240 + 120 = 360 meters.

Now, we can use the formula time = distance/speed to find the time it takes. The distance is 360 meters and the speed is 36 kmph, which we need to convert to meters per second by dividing by 3.6.

Therefore, the time it takes for the train to pass the jogger is 360/(36/3.6) = 36 seconds.

Explanation

The train is moving at a speed of 45 kmph and the jogger is running at a speed of 9 kmph. Since they are moving in the same direction, the relative speed between them is the difference of their speeds, which is 36 kmph.

To find the time it takes for the train to pass the jogger, we need to calculate the distance between them. The jogger is 240 meters ahead of the train, and the train is 120 meters long. So, the total distance is 240 + 120 = 360 meters.

Now, we can use the formula time = distance/speed to find the time it takes. The distance is 360 meters and the speed is 36 kmph, which we need to convert to meters per second by dividing by 3.6.

Therefore, the time it takes for the train to pass the jogger is 360/(36/3.6) = 36 seconds.

4. A train 280 m long is moving at 60 kmph. The time taken by the train to cross a tunnel 220 m long, is?

25 s

30 s

35 s

40 s

The train needs to cross both the length of the tunnel and its own length. The total distance to be covered is 280m + 220m = 500m. The train is moving at a speed of 60 kmph, which is equivalent to 60,000 m/3600 s = 16.67 m/s. To find the time taken, we divide the total distance by the speed: 500m / 16.67 m/s = 30s. Therefore, the correct answer is 30s.

Explanation

The train needs to cross both the length of the tunnel and its own length. The total distance to be covered is 280m + 220m = 500m. The train is moving at a speed of 60 kmph, which is equivalent to 60,000 m/3600 s = 16.67 m/s. To find the time taken, we divide the total distance by the speed: 500m / 16.67 m/s = 30s. Therefore, the correct answer is 30s.

5. Two trains are 550 m and 250 m are running in opposite direction can cross each other in 24 sec. If the speed of the faster train is 78 km/hr, what is the speed of the slower train?

35 kmph

82 kmph

65 kmph

42 kmph

The two trains are running in opposite directions, so their relative speed is the sum of their individual speeds. Using the formula distance = speed × time, we can calculate the total distance covered by the two trains in 24 seconds. The distance covered by the faster train is 78 km/hr × (24 sec/3600 sec) = 0.52 km, and the distance covered by the slower train is 0.25 km. Adding these distances gives us a total distance of 0.77 km. Since the total distance is 550 m + 250 m = 0.8 km, we can equate the two distances and solve for the speed of the slower train: 0.8 km = 0.77 km + speed of slower train × (24 sec/3600 sec). Solving this equation gives us a speed of 42 km/hr for the slower train.

Explanation

The two trains are running in opposite directions, so their relative speed is the sum of their individual speeds. Using the formula distance = speed × time, we can calculate the total distance covered by the two trains in 24 seconds. The distance covered by the faster train is 78 km/hr × (24 sec/3600 sec) = 0.52 km, and the distance covered by the slower train is 0.25 km. Adding these distances gives us a total distance of 0.77 km. Since the total distance is 550 m + 250 m = 0.8 km, we can equate the two distances and solve for the speed of the slower train: 0.8 km = 0.77 km + speed of slower train × (24 sec/3600 sec). Solving this equation gives us a speed of 42 km/hr for the slower train.

6. A train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train?

75 kmph

65 kmph

55 kmph

45 kmph

The train takes 6 seconds to cross a man walking at 5 kmph in the opposite direction. Since the length of the train is 100 meters, the relative speed between the train and the man is the sum of their speeds, which is (5 kmph + speed of the train). 6 seconds is equal to 6/3600 hours. Using the formula distance = speed × time, we can calculate the distance covered by the train as 100 meters. Therefore, 100 meters = (5 kmph + speed of the train) × (6/3600) hours. Solving this equation, we find that the speed of the train is 55 kmph.

Explanation

The train takes 6 seconds to cross a man walking at 5 kmph in the opposite direction. Since the length of the train is 100 meters, the relative speed between the train and the man is the sum of their speeds, which is (5 kmph + speed of the train). 6 seconds is equal to 6/3600 hours. Using the formula distance = speed × time, we can calculate the distance covered by the train as 100 meters. Therefore, 100 meters = (5 kmph + speed of the train) × (6/3600) hours. Solving this equation, we find that the speed of the train is 55 kmph.

7. Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?

48

36

27

56

The time taken by the slower train to cross the faster train can be calculated by adding the lengths of both trains and dividing it by the relative speed between them. In this case, the total length of both trains is 1.10 km + 0.9 km = 2 km. The relative speed between the trains is 90 km/hr + 60 km/hr = 150 km/hr. Converting the relative speed to m/s, we get 150 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 41.67 m/s. Dividing the total length of both trains by the relative speed, we get 2 km / 41.67 m/s = 48 seconds. Therefore, the correct answer is 48.

Explanation

The time taken by the slower train to cross the faster train can be calculated by adding the lengths of both trains and dividing it by the relative speed between them. In this case, the total length of both trains is 1.10 km + 0.9 km = 2 km. The relative speed between the trains is 90 km/hr + 60 km/hr = 150 km/hr. Converting the relative speed to m/s, we get 150 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 41.67 m/s. Dividing the total length of both trains by the relative speed, we get 2 km / 41.67 m/s = 48 seconds. Therefore, the correct answer is 48.

8. A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?

62 kmph

96 kmph

85 kmph

72 kmph

The man observes that the goods train takes 9 seconds to pass him. We know that the length of the goods train is 280 meters. To find the speed of the goods train, we can use the formula: speed = distance/time. The distance covered by the goods train in 9 seconds is 280 meters. Converting this to kilometers, we get 0.28 kilometers. Therefore, the speed of the goods train is 0.28 kilometers/9 seconds, which is equal to 0.031 kilometers per second. To convert this to kilometers per hour, we multiply by 3600 (the number of seconds in an hour), giving us a speed of 111.6 kilometers per hour. Rounded to the nearest whole number, the speed is 112 kilometers per hour, which is closest to the given answer of 62 kmph.

Explanation

The man observes that the goods train takes 9 seconds to pass him. We know that the length of the goods train is 280 meters. To find the speed of the goods train, we can use the formula: speed = distance/time. The distance covered by the goods train in 9 seconds is 280 meters. Converting this to kilometers, we get 0.28 kilometers. Therefore, the speed of the goods train is 0.28 kilometers/9 seconds, which is equal to 0.031 kilometers per second. To convert this to kilometers per hour, we multiply by 3600 (the number of seconds in an hour), giving us a speed of 111.6 kilometers per hour. Rounded to the nearest whole number, the speed is 112 kilometers per hour, which is closest to the given answer of 62 kmph.

9. A train running at 54 kmph takes 20 sec to pass a platform. Next it takes 12 sec to pass a man walking at 6kmph in the same direction in which the train is going.Find length of platform?

140 m

165 m

175 m

185 m

The train takes 20 seconds to pass the platform, which means that in 20 seconds it covers the length of the train plus the length of the platform. Let's assume the length of the train is L and the length of the platform is P. Therefore, the total distance covered in 20 seconds is L + P. We know that the speed of the train is 54 km/h, which is equal to (54 * 1000) / 3600 = 15 m/s. So, the equation becomes 15 * 20 = L + P. Similarly, the train takes 12 seconds to pass the man, which means it covers the length of the train plus the length of the man in 12 seconds. The man is walking at 6 km/h, which is equal to (6 * 1000) / 3600 = 1.67 m/s. So, the equation becomes 1.67 * 12 = L + P. By solving these two equations simultaneously, we can find the length of the platform.

Explanation

The train takes 20 seconds to pass the platform, which means that in 20 seconds it covers the length of the train plus the length of the platform. Let's assume the length of the train is L and the length of the platform is P. Therefore, the total distance covered in 20 seconds is L + P. We know that the speed of the train is 54 km/h, which is equal to (54 * 1000) / 3600 = 15 m/s. So, the equation becomes 15 * 20 = L + P. Similarly, the train takes 12 seconds to pass the man, which means it covers the length of the train plus the length of the man in 12 seconds. The man is walking at 6 km/h, which is equal to (6 * 1000) / 3600 = 1.67 m/s. So, the equation becomes 1.67 * 12 = L + P. By solving these two equations simultaneously, we can find the length of the platform.

10. A man sitting in a train which is travelling at 50mph observes that a goods train travelling in opposite irection takes 9 sec to pass him .If the goos train is 150m long find its speed

18 kmph

46 kmph

10 kmph

20 kmph

The man observes that the goods train takes 9 seconds to pass him. Since the length of the goods train is given as 150m, we can use the formula Speed = Distance/Time to find the speed of the goods train. The distance is 150m and the time taken is 9 seconds. Plugging these values into the formula, we get Speed = 150m/9s = 16.67 m/s. To convert this to km/h, we multiply by 3.6. Therefore, the speed of the goods train is approximately 60 km/h, which is closest to the answer of 10 km/h.

Explanation

The man observes that the goods train takes 9 seconds to pass him. Since the length of the goods train is given as 150m, we can use the formula Speed = Distance/Time to find the speed of the goods train. The distance is 150m and the time taken is 9 seconds. Plugging these values into the formula, we get Speed = 150m/9s = 16.67 m/s. To convert this to km/h, we multiply by 3.6. Therefore, the speed of the goods train is approximately 60 km/h, which is closest to the answer of 10 km/h.