Problem on Trains
- A train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in 25 second. Its length in meters is ?
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Let the length of the train be 'L' meters and its speed be 'v' meters/sec
Then, L/v = 15
⇒ v = L/15 ....(1)
Now, (L + 100)/25 = L/15
⇒ L = 150 mCorrect Option: B
Let the length of the train be 'L' meters and its speed be 'v' meters/sec
Then, L/v = 15
⇒ v = L/15 ....(1)
Now, (L + 100)/25 = L/15
⇒ L = 150 m
- A train 100 meter long moving at a speed of 50 kmph crosses a train 120 meters long coming from opposite direction in 6 seconds. The speed of second train is ?
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Let the speed of the second train be y km/hr
Relative speed of both trains = (50 + y) km/hr
Total distance traveled = 100 + 120 = 220 meters = 0.22 km
Time = 6 sec = 6/( 60 x 60) hr.
Speed = distance/timeCorrect Option: B
Let the speed of the second train be y km/hr
Relative speed of both trains = (50 + y) km/hr
Total distance traveled = 100 + 120 = 220 meters = 0.22 km
Time = 6 sec = 6/( 60 x 60) hr.
Speed = distance/time
⇒ 50 + y = (0.22 x 60 x 60)/ 6
⇒ 50 + y = 132
∴ y = 82
∴ Speed of the second train = 82 km/hr
- 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 ?
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Let the length of the train be L km and its speed by y km/hr
Then , speed of train relative to first man = (y - 2) km/hr
Speed of train relative to second man = (y - 4) km/hr
∵ L / (y - 2) = 9 /(60 x 60)
and L / (y - 4) = 10/ (60 x 60)Correct Option: C
Let the length of the train be L km and its speed by y km/hr
Then , speed of train relative to first man = (y - 2) km/hr
Speed of train relative to second man = (y - 4) km/hr
∵ L / (y - 2) = 9 /(60 x 60)
and L / (y - 4) = 10/ (60 x 60)
∴ 9y - 18 = 3600 x L ...(1)
and 10y - 40 = 36000 x L ... (2)
So, 9y - 18 = 10y - 40
⇒ y = 22
∵ L/ (22 - 2) = 9/ 3600
∴ L = (20 x 9) / 3600 = 1/20 km = (1/20) x 1000 = 50 m.
- Two stations A and B are 110 kms apart on a straight line. One train start from A at 7 a.m. and travels towards B at 20 km per hour speed. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 km per hour. At what time will they meet ?
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Suppose they meet T hrs after 7 a.m
∴ Distance covered by A in T hrs = (20 x T) km
Distance covered by B in (T - 1) hrs = 25(T - 1) km
From question 20T + 25 (T -1) = 110Correct Option: B
Suppose they meet T hrs after 7 a.m
∴ Distance covered by A in T hrs = (20 x T) km
Distance covered by B in (T - 1) hrs = 25(T - 1) km
∵ 20T + 25 (T -1) = 110
⇒ 45 x T = 135
∴ T = 3 hours
So, they meet at 10 a.m.
- A train 75 meters long is running with a speed of 20 km/hr. It will pass a standing man in ?
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∵ Speed of the train = (20 x 5/18) = (50/9) m/sec
Correct Option: B
∵ Speed of the train = 20 x (5/18) = (50/9) m/sec
∴ Time taken by the train to pass the man = 75 x (9/50) = 13.5 sec
