1.
Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms?
Correct Answer
C. 120 kmph
2.
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Correct Answer
A. 3:2
Explanation
The ratio of the speeds of the two trains can be determined by using the concept of relative speed. When the two trains are moving in opposite directions, their speeds are added. When they cross each other, their speeds are subtracted. Let's assume the speeds of the two trains are 3x and 2x respectively. When they are moving in opposite directions, the relative speed is 3x + 2x = 5x. The time taken to cross the man is 27 seconds, so the distance covered is 27 * 5x = 135x. Similarly, when they cross each other, the relative speed is 3x - 2x = x. The time taken to cross each other is 23 seconds, so the distance covered is 23 * x = 23x. Since the two distances are the same, we can equate them: 135x = 23x. Solving this equation gives x = 2. Therefore, the ratio of the speeds is 3x:2x = 3:2.
3.
A train 150 m long is running with a apecd of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
Correct Answer
B. 9 sec
Explanation
The train is running faster than the man, so it will eventually pass him. To calculate the time it takes for the train to pass the man, we need to find the relative speed between the train and the man. The relative speed is the difference between the speed of the train and the speed of the man, which is (68 kmph - 8 kmph) = 60 kmph.
We need to convert this relative speed to meters per second, so we divide by 3.6 (since 1 kmph = 1000/3600 m/s).
60 kmph / 3.6 = 16.67 m/s.
Now, we can calculate the time it takes for the train to pass the man by dividing the length of the train (150 m) by the relative speed (16.67 m/s):
150 m / 16.67 m/s ≈ 9 sec.
Therefore, the train will pass the man in approximately 9 seconds.
4.
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the
train?
Correct Answer
B. 150 m
Explanation
The length of the train can be calculated using the formula: Length = Speed x Time. In this case, the speed of the train is given as 60 km/hr and the time taken to cross the pole is 9 seconds. To calculate the length, we need to convert the speed from km/hr to m/s, which is 60 km/hr = 60 x (1000/3600) m/s = 16.67 m/s. Plugging in the values, Length = 16.67 m/s x 9 s = 150 m. Therefore, the length of the train is 150 m.
5.
A train 150 m long is running at a speed of 90kmph. Time taken by
the train to cross a tree is?
Correct Answer
D. 6
Explanation
The time taken by the train to cross a tree can be calculated by dividing the distance traveled by the train (150 m) by its speed (90 km/h). First, we convert the speed from km/h to m/s by dividing it by 3.6 (1 km/h = 0.2778 m/s). So, the speed of the train is 25 m/s. Dividing the distance (150 m) by the speed (25 m/s) gives us the time taken, which is 6 seconds.
6.
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Correct Answer
A. 240 m
Explanation
The length of the platform can be determined by subtracting the distance covered by the train in 20 seconds from the distance covered by the train in 36 seconds. The train covers a distance of 54 km/hr in 36 seconds, which is equal to 54000/3600 = 15 m/s. Therefore, the train covers a distance of 15 m/s x 36 s = 540 m in 36 seconds. Similarly, the train covers a distance of 15 m/s x 20 s = 300 m in 20 seconds. Subtracting the distance covered in 20 seconds from the distance covered in 36 seconds gives us the length of the platform, which is 540 m - 300 m = 240 m.
7.
A train moves with a speed of 108 kmph.Its speed in metres per second is?
Correct Answer
B. 30
Explanation
To convert the speed from kilometers per hour to meters per second, we need to multiply it by 1000/3600. In this case, the train's speed of 108 kmph would be equal to (108 * 1000) / 3600 = 30 meters per second.
8.
A train 100 m long is running at the speed of 30 km / hr. Find the time
taken by it to pass a man standing near the railway line.
Correct Answer
D. 12 sec
Explanation
The time taken by the train to pass the man can be calculated using the formula: time = distance/speed. The distance the train needs to cover to pass the man is equal to its own length, which is 100 m. The speed of the train is given as 30 km/hr. To convert this to m/s, we divide by 3.6 (1 km/hr = 1000 m/3600 s). Therefore, the speed of the train is 8.33 m/s. Substituting these values into the formula, we get time = 100 m / 8.33 m/s = 12 sec.
9.
Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is?
Correct Answer
C. 180 m
Explanation
The man in the slower train passes the faster train in 8 seconds, which means that in 8 seconds, the faster train travels a distance equal to its own length plus the length of the slower train. Since the slower train is traveling at 36 kmph and the faster train is traveling at 45 kmph, the relative speed between the two trains is 36 + 45 = 81 kmph. Converting this to meters per second gives us 81 * (5/18) = 45/2 m/s. Therefore, in 8 seconds, the faster train travels a distance of (45/2) * 8 = 180 meters. Hence, the length of the faster train is 180 meters.
10.
A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going ?
Correct Answer
C. 12 sec
Explanation
The train is moving in the opposite direction of the man, so their relative speed is the sum of their speeds, which is (59 kmph + 7 kmph) = 66 kmph. We need to convert this speed to meters per second, so we divide by 3.6: (66 kmph / 3.6) = 18.33 m/s. The time taken to pass the man is equal to the distance traveled by the train, which is 220 m, divided by the relative speed: (220 m / 18.33 m/s) = 12 sec.