# Aptitude Problem on Trains Test Paper 4

16) A train moving at 108 km/hr crosses a platform in 30 seconds. Then it crosses a man running at 12 km/hr in the same direction of train in 9 seconds. What is the length of train and platform?

1. 220 & 600
2. 200 & 620
3. 240 & 660
4. 250 & 640

The correct option is (C).

Let the length of train X meters and length of platform Y meters

Relative Speed (Speed of train relative to man) = 108 − 12 = 96 km/hr

Relative Speed in m/sec = 96 x The distance covered by train to cross the man is equal to its length. So, it is = X meters

So, X = Relative Speed x Time (time taken to cross the man) * 9 = 240 meters (length of train)

Speed of train in m/s = 108 x Time taken to cross the platform = So, 30= 900 = 240 + y

Y= 900 − 240 = 660 meters (length of platform)

17) A train crosses two men who are running in the direction of train at 4 km/hr and 8 km/hr in 18 and 20 seconds respectively. Find the length of train.

1. 160 meters
2. 175 meters
3. 190 meters
4. 200 meters

The correct option is (D).

First man speed = 4 * Second man speed= 8 * Let the length of train is X meters and its speed is Y m/s

Time =  162 Y - 180 = 9X ..... (1) and 180Y - 400 = 9X .....(2)

From equation (2): 180Y = 9X + 400

Y = Insert the value of Y in equation (1) 1458X + 64800 - 32400 = 1620 X

32400 = 162 X

X = = 200 meters

18) Two trains of length 125 meters and 115 meters are running on parallel tracks. When they run in the same direction the faster train crosses the slower train in 30 seconds and when they run in opposite direction they cross each other in 10 seconds. What is the speed of each train?

1. 20,5
2. 18,6
3. 16,8
4. 14,7

The correct option is (C).

Let the speed of faster train = X m/sec

Let the speed of slower train= Y m/sec

Then, relative speed when they are moving in opposite direction = X + Y 10X + 10Y = 240

X + Y = 24

Y = 24 − X ................ (1)

Relative speed when they are moving in same direction = X − Y 30X − 30Y = 240

3X − 3Y = 24

X − Y = 8 ............... (2)

Put the value of Y from equation (1) to equation (2)

X − (24 − X) = 8

X − 24 + X = 8

2X = 8 + 24

2X = 32

X = 16 m/sec

Put the value of X in equation (1) to find value of Y;

Y = 24-16 = 8 m/sec.

19) Two stations P and Q are 160 km apart on a straight track. A train starts running from station P at 8 a.m. at a speed of 30 km/hr towards station Q. Another train starts from station Q at 9 a.m. at a speed of 35 km/hr towards station P. At what time they will meet?

1. 10 a.m.
2. 11 a.m.
3. 12 a.m.
4. 1 p.m.

The correct option is (B).

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

Distance covered by train starting from station P = speed * time

So, distance = 30 * X = 30X km

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 -1) = 160

30X + 35X - 35 = 160

65X = 160 +35

65X = 195 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.

20) Two trains are moving towards each other with speeds 40 km/hr and 45 km/hr from different stations P and Q. When they meet the second train from station Q has covered 20 km more distance than the first train which starts from station P. What is the distance between the two stations?

1. 300 km
2. 320 km
3. 340 km
4. 360 km

The correct option is (C).

The distance between the stations is equal to the sum of distance covered by each train.

Let the distance covered by first distance = X

So, the distance covered by second train = X + 20

When the two trains starts from two different stations at the same time towards each other, they take same time to meet each other. 45X = 40X + 800

45X − 40X = 800

5X = 800 Then distance covered by second train = 160 + 20 =180 km

So, the distance between stations P and Q = 160 + 180 = 340 km

Problem on Trains Aptitude Test Paper 1
Problem on Trains Aptitude Test Paper 2
Problem on Trains Aptitude Test Paper 3
Problem on Trains Aptitude Test Paper 5
Problem on Trains Concepts

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