Aptitude Problem on Trains Test Paper 4

The correct option is (C).

Answer with explanation:

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)

The correct option is (D).

Answer with explanation:

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

The correct option is (C).

Answer with explanation:

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.

The correct option is (B).

Answer with explanation:

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.

The correct option is (C).

Answer with explanation:

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