Train Problems - Solved Problem

Train Problems - Solved Problem - 1

Question 1
A train of length 150 meters can cross a bridge in 30 seconds when travelling at a speed of 40km/hr. Then what is the length of the bridge?
a)180m b)182 c)183 d)185
Answer : c)183
Solution:
Let the length of the bridge be X.
The speed of the train = 40km/hr = 40 x 5/18 m/sec = 100/9 m/sec.
The time taken to cross the bridge = 30 seconds.
Then, [150 + X ] / 30 = 100/9
150 + X = 3000 /9
X = 3000/9 - 150 = 1650/9 = 183.33
Hence the answer is 183 m.


Question 2
A train crosses a bridge and a bike standing on the bridge in 40 seconds, 25 seconds respectively. What is the length of the bridge if the speed of the train is 50.4km/hr?
a)180m b)210 c)183 d)185
Answer : b)210
Solution:
Given that,
The speed of the train = 50.4km/hr = 50.4 x 5/18 m/sec = 14 m/sec
The train crosses a bike(standing object) in 25 seconds.Then,
Length of the train = (14 x 25)m = 350 m.
Now, let the length of the bridge is X m.
the train crosses the bridge in 40 seconds.
Then, (X + 350)/40 = 14
X + 350 = 14 x 40 = 560
X = 210
Hence the bridge is 210m long.


Question 3
In what time a train 120 meters long travelling at a speed of 70km/hr crosses a cyclist who is at the speed 5km/hr in the direction opposite to the train?
a)4.76sec b)5.76sec c)8.92sec d)6.14sec
Answer : b)5.76sec
Solution:
Given that the speed of the train and a cyclist is 70km/hr and 5km/hr respectively.
Then, the Speed of train relative to cyclist = (70 + 5) km/hr = 75 km/hr = 75 x 5/18 = 125/6 m/sec.
The time taken to cross the cyclist = 120 / (125/6) = 120 x 6/125 =5.76 sec
hence the answer is 5.76 seconds.


Question 4
A train overtakes two bikes which are travelling at the speed of 25km/hr and 30km/hr in the same direction the train is moving and crosses them in 18 and 21 seconds respectively. Then the length of the train is:
a)170m b)175m c)173m d)185m
Answer : b)175
Solution:
Let us convert the speed in the unit of m/sec
25km/hr = 25 x 5/18 = 125/18 m/sec
and 30km/hr = 30 x 5/18 = 150/18 m/sec.
Let the length of the train be X metres and its speed by Y m/sec
Then the relative speed of the train and the bike with speed 125/18 m/sec is (Y - 125/18)
And the relative speed of the train and the bike with speed 150/18 m/sec is (Y - 150/18).
Then we can express the time taken to pass the bike as
[X / (Y - 125/18) ] = 18 and [ X / (Y - 150/18 )] = 21
By Simplifying above we get, X = 18Y - 125
and X = 21Y - 175
Solving the eqns we get Y = 50/3 and X = 175.
Hence the length of the train is 175m.


Question 5
A train 200 m long is moving with the speed of 50km per hour.Find the time taken to pass a tree standing near the railway track.
a)14 2/5 seconds b)15 seconds c)16 1/2 seconds d)17 seconds
Answer : a)14 2/5 seconds
Solution:
Speed of the train = 50km/hr = 50 x 5/18 m/sec = 250/18 m/sec
Length of the train = 200 m
Time taken to cross the tree = 200 / (250/18) = 200 x 18/250 = 72/5 = 14.4 seconds
Hence the answer is 14 2/5 seconds.


Question 6
A train of length 80 m. If the speed of the train is 120km/hr, then the time taken to cross a 150 m long wall is:
a)5 seconds b)3 seconds c)7 seconds d)6 seconds
Answer: c)7 seconds
Solution:
speed of the train = 120 km/hr = 120 x5/18 m/sec = 100/3 m/sec
Distance covered in passing the long wall = (80+150) = 230 m
Time taken to cross the wall = 230 x 3/100 = 6.9 sec
Hence the answer is 7 seconds(approximately)


Question 7
A bike and the train are running at a speed of 15km/hr and 70km/hr. The length of the train is 200m.Find the time taken by the train to cross the bike.
a)11seconds b)10seconds c)9seconds d)13seconds
Answer : d)13 seconds
Solution:
Speed of the train relative to bike (70 - 15) = 55km/hr = 55 x 5/18 m/sec = 275/18 m/sec
Time taken to cross the bike = time taken to cross 200 m at 275/18 m/sec
= 200 x 18/275 = 8 x 18/11 = 13.09 seconds.
Hence the answer is 13 seconds(approximately)


Question 8
Find the approximate speed of a train which passes a tree in 12 seconds. Note that the length of the train is 264m.
a) 79 km/hr b) 80 km/hr c) 84 km/hr d) 74 km/hr
Answer : a) 79 km/hr
Solution:
Length of the train = 264m.
Time taken to pass the tree = 12 seconds.
Speed of the train = 264/12 m/sec = 22 m/sec = 22 x 18/5 km/hr = 79.2 km/hr.
Hence the answer is 79 km/hr.(approximately).


Question 9
A train crosses a standing man in 3 seconds and moves at a rate of 120 km/hr. Find the length of the train.
a) 200 m b) 98 m c) 260 m d) 100 m
Answer : d) 100 m
Solution :
Speed of the train = 120 km/hr = 120 x 5/18 m/s.
=100/3 m/sec.
Time taken to cross the standing man is 3 seconds.
Length of the train = Speed of the train x Time taken to cross the standing man
= 3 x 100/3 = 100 m.
Hence the train is 100 m long.


Question 10
A 480 m long train crosses a standing object in 12 seconds. Find the time taken by the train to cross a long wall of length 325 m.
a) 20 sec b) 15 sec c) 19 sec d) 21 sec
Answer : a) 20 sec
Solution :
Length of the train = 480 m
Time taken to cross an object = 12 seconds.
Speed of the train = Length of the train / Time taken to cross an object = 480/12 m/sec = 40 m/sec.
Length of the wall = 325 m
Time taken to cross the wall = (Length of the train + Length of the wall) / Speed of the train
= (480 + 325 m)/40 seconds = 805/40 = 20.12 seconds
Hence the answer is 20 seconds.


Question 11
A train crosses a long river of length 6 km and a standing man in 300 seconds and 12 seconds respectively. What will be the length of the train?
a) 170 m b) 240 m c) 150 m d) 190 m
Answer : b) 240 m
Solution :
Time taken to cross the river(6 km) = 300 seconds.
Speed of the train = Distance / Time = 6 km / 300seconds = 6000/300 m/sec = 20 m/s
Train crosses a man in 12 seconds.
Length of the train = Speed of the train x Time Taken to cross the river = 20 x 12 = 240m
Hence the required length is 240 m.


Question 12
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 13
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 14
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 15
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


Question 16
If a train of length 300 meters takes 81 seconds to cover a 600 meters wall then which of the following will be its speed in km/hr?
a) 38 b) 42 c) 35 d) none of these
Answer : d) none of these
Solution:
By using the formula 4,
Time taken by a train of length 300 meters to pass a wall of length 600 meters is the time taken by the train to covers (300+600) meters.
That is, 81 seconds.
We know that, distance/time = speed
Therefore, required speed = (300+600)/81 m/sec
= 900/81 m/sec
Converting the above to km/hr, by using formula 2,
= (900/81)x(18/5) km/hr
= 40 km/hr.
Hence the answer is option d.


Question 17
A train takes 120 seconds to cover a distance of length 200 meters at a speed of 90km/hr. What will be the time taken by the train to cross a standing man?
a) 120 seconds b) 108 seconds c) 112 second d) none of these
Answer : c) 112 second
Solution:
Speed of the train = 90km/hr.
Converting the speed into m/sec: by using formula 1,
Speed = 90 km/hr = 90 x 5/18 m/sec = 25 m/sec
First, we have to find the length of the train.
Let the length of the train be X km.
Given that, the time taken to cover 200 meters = 120 seconds.
From the formula 4,
We can have (X+200)/25 = 120 (distance/speed = time)
X+200 = 120x25 = 3000
X = 2800 meters.
Now, using formula 3, the time taken by the train of length 2800 meters to cross a standing man at 25 m/sec = 2800 / 25 seconds = 112 seconds.
Hence the answer is option c.


Question 18
A train takes 72 seconds and 40 seconds to cross a platform and a pole respectively. If the train runs at 108 km/hr then length of the platform is:
a) 960 meters b) 1020 meters c) data inadequate d) none of these
Answer : a) 960 meters
Solution :
Speed of the train = 108km/hr.
Converting the speed into m/sec: by using formula 1,
Speed = 108 km/hr = 108 x 5/18 m/sec = 30 m/sec
Given that the time taken to cross a Pole = 40 seconds.
Therefore, length of the train = speed x time = 30 x 40 = 1200 meters.
Let the length of the platform be X meters.
The time taken to cross the platform at 30 m/sec = 72 seconds
by using the formula 4, we have,
(X+1200)/72 = 30
(X+1200) = 2160
X = 960
Hence the required length is 960 meters.


Question 19
If a train crosses a tree in 36 seconds, then the distance which the train of length 600 meters can cover in 78 seconds, is:
a) 400 meters b) 500 meters c) date inadequate d) none of these
Answer : d) none of these.
Solution :
Given that,
Length of the train = 600 meters.
Time taken to cross a tree = 36 seconds.
Therefore, speed of the train = 600/36 = 50/3 m/sec.
Let the required distance be X meters.
Then, the time taken to cover X meters = 78 seconds.
Form the formula 4, we have,
(X+600)/78 = 50/3
X+600 = 50x78/3 = 1300
X = 1300-600 = 700 m.
Hence the required answer is option d.