Practice Problems on Trains – Set 1
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
Answer:
C)
Explanation:
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.
2. Two trains 300m and 400m long run at the speeds of 40 kmph and
50kmph respectively in opposite Directions on parallel tracks. The time
taken to cross each other?
a)
20 sec
b)
25 sec
c)
26 sec
d)
28 sec
Answer:
D)
Explanation:
Length of two Trains = 300m + 400m = 700m
Total Speed= 40 Kmph + 50 Kmph (Opposite Direction) =
90 Kmph
Time = Distance/Speed
Time = 700/ 90
Time = 28Sec
3. A 270 metres long train running at the speed of 120 kmph crosses another
train running in opposite direction at the speed of 80 kmph in 9 seconds. What
is the length of the other train ?
a) 230 m
b) 240 m
c) 260 m
d) 320 m
Answer:
A)
Explanation:
Relative speed = (120 + 80) km/hr = 200 kmph = 200 ×
5/18 = 500/9 mph
Let the length of the other train be x metres.
Then, (270 + x)/9 = 500/9 => x = 500 – 270 = 230
4. Two trains are moving in opposite directions at 60 km/hr and 90
km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the
slower train to cross the faster train in seconds is:
a) 58 sec
b) 50 sec
c) 48 sec
d) 56 sec
Answer:
C)
Explanation:
Relative speed = all lengths/time
[60+90] = [1.10 +0.9 ]/time [ PLUS when opposite
direction] time=2/150 = 1/75 h
1 hour______3600 sec
1/75 hr______?
?= 3600/75=48 sec
5. 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)
Explanation:
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.
6. A train overtakes two persons who are walking in the same direction
in which the train is going, at the rate of 2 kmph and 4 kmph and passes them
completely in 9 and 10 seconds respectively. The length of the train is:
a) 45m
b) 55m
c) 50m
d) 60m
Answer:
C)
Explanation:
2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.
4 kmph = (4 x 5/18 m/sec = 10/9 m/sec.
Let the length of the train be x metres and its
speed by y m/sec.
Then, ( x/(y - 5) = 9 and ( x/(y - 10) = 10.
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
7. A train moves past a telegraph post and a bridge 264 m long in 8
seconds and 20 seconds respectively. What is the speed of the train ?
a) 69.5 kmph
b) 70 kmph
c) 72 kmph
d) 79.2 kmph
Answer:
D)
Explanation:
Let the length of the train be x metres and its speed by y m/sec.
Then, x/y = 8 => x = 8y
Now, (x + 264)/20 = y
=> 8y + 264 = 20y
=> y = 22.
Speed = 22 m/sec = 22 × 18/5km/hr = 79.2 km/hr.
8. A train travelling at a speed of 75 mph enters a tunnel 7/2 miles
long. The train is 1/4 mile long. How long does it take for the train to pass
through the tunnel from the moment the front enters to the moment the rear
emerges?
A) 1 min
B) 3 min
C) 5 min
D) 6 min
Answer:
B)
Explanation:
Actually train is covering length of tunnel + its
own length here
so total distance = 7/2 + 1/4= 15/4 miles
time= distance /speed
time= (15/4) / 75 = 1/20 hour
(1/20)x60 = 3 min
9. The distance between two cities A and B is 330 km. A train starts
from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B
at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
A) 10:30 am
B) 10:45 am
C) 11 am
D) 11:25 am
Answer:
C)
Explanation:
Suppose they meet x hrs after 8 a.m.
Then, (Distance moved by first in x hrs) + [Distance
moved by second in (x-1) hrs] = 330
60x + 75(x – 1) = 330
x = 3
So, they meet at (8 + 3), i.e. 11 a.m
10. A train overtakes two persons walking along a railway track. The
first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs
8.4 and 8.5 seconds respectively to overtake them. What is the speed of the
train if both the persons are walking in the same direction as the train?
a) 96 kmph
b) 81 kmph
c) 51 kmph
d) 62 kmph
Answer:
B)
Explanation:
4.5 km/hr = ( 4.5 x 5/18 ) m/sec = 5/4 m/sec = 1.25
m/sec, and
5.4 km/hr = ( 5.4 x 5/18 ) m/sec = 3/2 m/sec = 1.5
m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train = ( 22.5 x 18/5 ) km/hr
= 81 km/hr.
