Quantitative Apptitude - Problems On Train Online Test 6

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.