Problems on train
1.
A train running at the speed of 60 km/hr crosses
a pole in 9 seconds. What is the length of the train?
Answer:
Speed of train = 60 Km/h = 60 x
5/18 = 50/3 m/s
Time taken to cross the pole = 9
secs
So, length of the train = speed x
time = (50/3) x 9 = 150 m
2.
A train 125 m long passes a man, running at 5
km/hr in the same direction in which the train is going, in 10 seconds. The
speed of the train is:
Answer:
Since the man is running in the
same direction of the train the relative speed will be (St – 5)
Time taken to cross =0. 125 / (St
– 25/18) = 10/3600
Or, St – 5 = (0.125 x 3600/10) =
45
Or, St = (45 + 5) = 50 km/hr
3.
The length of the bridge, which a train 130
metres long and travelling at 45 km/hr can cross in 30 seconds, is -------------------
Answer:
Total length the train has to
cross = 130 + Lb
Where Lb = length of the bridge
130 + Lb = 45 x (5/18) m/s x 30 s
= 25 x 15
Lb = 245 m
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4. 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 -----------------------
Answer:
Let the speed of the two trains
be A and B
Length of the trains are La and
Lb
Now, La = 27A, Lb = 17B
(La + Lb) = 23(A + B)
Therefore, 27A + 17B = 23(A +
B)
Or, 4A = 6B
Or, A/B = 3/2
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5. Two, trains, one from Howrah to
Patna and the other from Patna to Howrah, start simultaneously. After they
meet, the trains reach their destinations after 9 hours and 16 hours
respectively. The ratio of their speeds is
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Let the total distance be x
between Howrah to Patna. Let the two trains meet at distance y from Howrah. Let
speed of the trains be Va and Vb km/hr respectively.
Since they
start simultaneously, the time taken to meet will be same.
So, time taken
to meet = (y/Va) = (x – y)/Vb
Or, yVb = (x –
y)Va --------------- (1)
Also the time
taken for remaining journey is given,
Therefore, 16
= y/Vb and 9 = (x – y)/Va
Or, y = 16Vb
and x – y = 9Va ----- (2)
Substituting 2
in 1, we get
16Vb .Vb =
9Va.Va
Or, 4Vb = 3Va
-------- taking square root
Or, Va/Vb =
4/3
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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
ANSWER:
Let the speed of the train be V
Length of train = (V – 2)x
9/3600 km = (V – 4)x 10/3600
Solving, we get 9V – 18 = 10V –
40
Or, V = 22 Km/hr
So, length of train = (22 – 2) x 9/ 3600 km = 50
m
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