Aptitude :: Problems on Trains

Practice :: Problems on Trains - General Questions
Problems on Trains - General Questions

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21. A train overtakes two persons walking on a railway track. The first runs at a speed of 4.5 km/h. The other moves at a speed of 5.4 km/h. 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 running in the same direction as the train?
85 km/hr
83 km/hr
81 km/hr
90 km/hr
Answer: option C

apply the formula for converting km/hr to m/sec.

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

∵ Speed of the train = (22.5 x 18/5) km/hr = 81 km/hr.



22. A person sitting in a train running at 100 km/h saw a goods train running in the opposite direction to him. A goods train crosses the man in 8 seconds. If the length of the goods train is 300 metres, find its speed.
37 Km/hr
35 Km/hr
45 Km/hr
39 Km/hr
Answer: option B

Let the speed of goods train = X km/hr

The man sitting in train is also moving at the speed of train = 100 km/hr

So, the speed of goods train relative to man = distance covered to cross the man (length of goods train)/ time taken to cross the man

so, Relative speed = 300/8 m/s.

⟹ 300/8 x 18/5 = 5400/40 = 135 km/hr.

∵ Now, Relative speed = speed of train or man + speed of goods train

⟹ 135 = 100 + X

⟹ Or X = 135 - 100 = 35 km/hr



23. Two stations P and Q are on a straight track at a distance of 160 km. A train starts from station P towards station Q at the speed of 30 km/hr at 8 am. Another train starts from station Q at 9 a.m. towards station P at the speed of 35 km/h. What time will they meet?
11.30 a.m
10.30 a.m
13 a.m
11 a.m
Answer: option D

Let the trains meet X hours after the frist train starts from station P at 8 a.m.

Distance covered by train starting from station P = speed x time = 30 x X = 30X km/hr

Similarly, Distance covered by trains starting from Q = 35 * (X -1) km, as it starts running 1 hour later than the first train.

⟹ The distance between the two stations = 160 km

The sum of the distances travelled by both trains to meet each other will be equal to the distance between two stations.

∵ So, 30X + 35 x (X -1) = 160

⟹ 30X + 35X - 35 = 160

⟹ 65X = 160 + 35

⟹ 65X = 195

⟹ X = 195/65 = 3 hours

It means they will meet 3 hours after the first train starts at 8 a.m. So, they will meet at 8 + 3 = 11 a.m.




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