Quantitative Apptitude - Problems On Train Online Test 1

Explanation
The length of the train can be calculated using the formula: distance = speed × time. In this case, the speed of the train is given as 60 km/hr, which is equivalent to 60,000 m/3600 s = 16.67 m/s. The time taken to cross the pole is given as 9 seconds. Plugging these values into the formula, we get distance = 16.67 m/s × 9 s = 150 m. Therefore, the length of the train is 150 m.

Explanation
The time taken by the train to pass the man can be calculated using the formula: time = distance/speed. The distance here is the length of the train, which is given as 100 m. The speed of the train is given as 30 km/hr, which needs to be converted to m/s by dividing it by 3.6. Therefore, the speed is 8.33 m/s. Plugging these values into the formula, we get time = 100/8.33 = 12 sec. So, it will take 12 seconds for the train to pass the man standing near the railway line.

Explanation
The train is moving at a speed of 68 kmph, which is equivalent to 68 * (5/18) m/s. The man is running at a speed of 8 kmph, which is equivalent to 8 * (5/18) m/s. The relative speed of the train with respect to the man is the difference between the two speeds. Therefore, the relative speed is (68 * (5/18)) - (8 * (5/18)) = (340/18) m/s. To calculate the time it takes for the train to pass the man, we divide the length of the train (150 m) by the relative speed of the train. Therefore, 150 / (340/18) = 9 seconds.

Explanation
The man takes 8 seconds to cross the bridge, meaning the length of the bridge is covered in 8 seconds. The train takes 20 seconds to cross the bridge, meaning the length of the bridge plus the length of the train is covered in 20 seconds. Therefore, the length of the train is 20 seconds minus 8 seconds, which is 12 seconds. The length of the bridge is given as 180 m. So, the length of the train is 180 m. The speed of the train can be calculated by dividing the length of the train by the time taken to cross it, which is 180 m divided by 12 seconds, resulting in 15 m/s.

Explanation
The length of the train is given as 240 m and the speed at which it is running is given as 54 km/hr. To find the time it takes for the train to cross the tree, we need to convert the speed from km/hr to m/s. We can do this by dividing 54 by 3.6 (since 1 km/hr is equal to 3.6 m/s). This gives us a speed of 15 m/s. To find the time, we divide the length of the train (240 m) by the speed (15 m/s). The result is 16 seconds, which is the time it takes for the train to cross the tree.

Explanation
To convert the speed from kilometers per hour to meters per second, we need to multiply the speed in kilometers per hour by 1000/3600. By doing this calculation, we find that the speed of the train in meters per second is 30.

Explanation
The time taken by a train to cross a stationary object can be calculated using the formula: time = distance/speed. In this case, the distance is given as 180m and the speed is given as 72kmph. However, the speed needs to be converted to m/s by dividing it by 3.6. Therefore, the speed is 20m/s. Using the formula, we can calculate the time as 180/20 = 9 seconds. Therefore, the correct answer is 9 seconds.

Explanation
The train is passing a man who is running in the same direction as the train. In order to pass the man, the train needs to cover the length of the man, which is 125 meters. The time taken to cover this distance is given as 10 seconds. To find the speed of the train, we can use the formula speed = distance/time. Plugging in the values, we get speed = 125/10 = 12.5 meters per second. To convert this to kilometers per hour, we multiply by 3.6 (since 1 meter per second is equal to 3.6 kilometers per hour). Therefore, the speed of the train is 12.5 * 3.6 = 45 kmph.

Explanation
The time it takes for the train to cross the platform can be calculated by adding the time it takes for the train to cover its own length and the time it takes for the train to cover the length of the platform. The time it takes for the train to cover its own length can be calculated by dividing the length of the train by the speed of the train. The time it takes for the train to cover the length of the platform can be calculated by dividing the length of the platform by the speed of the train. Adding these two times together gives the total time it takes for the train to cross the platform.

Explanation
The time it takes for the two trains to be clear of each other from the moment they meet can be calculated by dividing the total distance traveled by the relative speed of the two trains. The total distance traveled is the sum of the lengths of the two trains, which is 137 + 163 = 300 meters. The relative speed of the two trains is the sum of their individual speeds, which is (42 + 48) km/h = 90 km/h. Converting this to meters per second, we get 90 * (1000/3600) = 25 m/s. Dividing the total distance traveled by the relative speed, we get 300 / 25 = 12 seconds. Therefore, the correct answer is 12 sec.