Dear Reader,
Below are four problems dealing with length, time and speed of a train.
Note :
1. To Convert km/hr to m/s : a km/hr = a x 5/18 m/s.
2. Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.
3. Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.
Question 1
A train, 300 meters long running at the rate of 68 km/hr will cross a lamp post in:
a) 12 seconds b) 14 seconds c) 16 seconds d) 18 seconds
Answer : c) 16 seconds.
Solution :
Speed of the train = 68 km/hr.
We have to find the time in seconds, so convert the speed in the unit of m/sec.
68 km/hr = 68 x 5/18 m/s = 170/9 m/s.
Length of the train = 300 meters.
From the note (2), we have to find the time taken by the train to cover 300 meters at 170/9 m/sec
Time = distance/speed = 300/(170/9) = 300 x 9/170 = 15.88.
Hence the answer is 16 seconds.
Question 2
If a train of length 175 meters takes 18 seconds to cross a bridge of length 275 meters, then the speed (in m/sec) of the train is:
a) 25 m/s b) 27 m/s c) 29 m/s c) 30 m/s
Answer : a) 25 m/s
Solution :
Length of the train = 175 meters
Length of the bridge = 275 meters
Time taken by the train too cross the bridge = 18 seconds.
From the note (3), we have to find the speed to cover (175 + 275) meters in 18 seconds.
Speed = distance/time = (175 + 275)/18 = 450/18 = 25 m/s.
Hence, the answer is 25.
Question 3
If a train of length 120 meters, crosses a tree in 6 seconds, then the time taken to covers 24 km by the train is: (in minutes)
a) 12 b) 20 c) 11 d) 14
Answer : b) 20.
Solution :
Length of the train = 120 meters.
Time taken to cross the tree = 6 seconds.
By using the note (1), we have the time taken by the train to cover 120 meters is 6 seconds.
Speed of the train = distance/time = 120/6 = 20 m/s.
Time taken to cover 24 km (24000 meters) = 24000/20 seconds = 1200 seconds.
Since, 60 seconds = 1 minute;
Then, 1200 seconds = 1200/60 = 20 minutes.
Hence, the answer is 20 minutes.
Question 4
If a train running at the speed of 8 1/3 m/s and covers 0.5 km long bridge in 2 minutes, then the length of the train is:
a) 0.4 km b) 0.3 km c) 0.25 km d) 0.5 km
Answer : d) 0.5 km
Solution :
Speed of the train = 8 1/3 = 25/3 m/s.
Length of the bridge = 0.5 km = 500 meters.
Time taken to cross the bridge = 2 minutes = 120 seconds.
Let the length of the train be X meters.
Time taken by the train to cover (500 + X) meters at 25/3 m/s is 120 seconds.
i.e., distance = speed x time
(500 + X) = 25/3 x 120
(500 + X) = 1000.
X = 1000 - 500 = 500 meters = 0.5 km.
Hence the length of the train is 0.5km
Below are four problems dealing with length, time and speed of a train.
Note :
1. To Convert km/hr to m/s : a km/hr = a x 5/18 m/s.
2. Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.
3. Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.
Question 1
A train, 300 meters long running at the rate of 68 km/hr will cross a lamp post in:
a) 12 seconds b) 14 seconds c) 16 seconds d) 18 seconds
Answer : c) 16 seconds.
Solution :
Speed of the train = 68 km/hr.
We have to find the time in seconds, so convert the speed in the unit of m/sec.
68 km/hr = 68 x 5/18 m/s = 170/9 m/s.
Length of the train = 300 meters.
From the note (2), we have to find the time taken by the train to cover 300 meters at 170/9 m/sec
Time = distance/speed = 300/(170/9) = 300 x 9/170 = 15.88.
Hence the answer is 16 seconds.
Question 2
If a train of length 175 meters takes 18 seconds to cross a bridge of length 275 meters, then the speed (in m/sec) of the train is:
a) 25 m/s b) 27 m/s c) 29 m/s c) 30 m/s
Answer : a) 25 m/s
Solution :
Length of the train = 175 meters
Length of the bridge = 275 meters
Time taken by the train too cross the bridge = 18 seconds.
From the note (3), we have to find the speed to cover (175 + 275) meters in 18 seconds.
Speed = distance/time = (175 + 275)/18 = 450/18 = 25 m/s.
Hence, the answer is 25.
Question 3
If a train of length 120 meters, crosses a tree in 6 seconds, then the time taken to covers 24 km by the train is: (in minutes)
a) 12 b) 20 c) 11 d) 14
Answer : b) 20.
Solution :
Length of the train = 120 meters.
Time taken to cross the tree = 6 seconds.
By using the note (1), we have the time taken by the train to cover 120 meters is 6 seconds.
Speed of the train = distance/time = 120/6 = 20 m/s.
Time taken to cover 24 km (24000 meters) = 24000/20 seconds = 1200 seconds.
Since, 60 seconds = 1 minute;
Then, 1200 seconds = 1200/60 = 20 minutes.
Hence, the answer is 20 minutes.
Question 4
If a train running at the speed of 8 1/3 m/s and covers 0.5 km long bridge in 2 minutes, then the length of the train is:
a) 0.4 km b) 0.3 km c) 0.25 km d) 0.5 km
Answer : d) 0.5 km
Solution :
Speed of the train = 8 1/3 = 25/3 m/s.
Length of the bridge = 0.5 km = 500 meters.
Time taken to cross the bridge = 2 minutes = 120 seconds.
Let the length of the train be X meters.
Time taken by the train to cover (500 + X) meters at 25/3 m/s is 120 seconds.
i.e., distance = speed x time
(500 + X) = 25/3 x 120
(500 + X) = 1000.
X = 1000 - 500 = 500 meters = 0.5 km.
Hence the length of the train is 0.5km
