Model 1 Train Vs Train in same direction Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on trains topic of quantitative aptitude

Questions : Two trains start from a certain place on two parallel tracks in the same direction. The speed of the trains are 45 km/hr. and 40 km/ hr respectively. The distance between the two trains after 45 minutes will be

(a) 2.75 km.

(b) 3.7 km.

(c) 3.75 km.

(d) 2.5 km.

The correct answers to the above question in:

Answer: (c)

Relative speed = 45 – 40 = 5 kmph.

Gap between trains after 45 minutes

= $(5 × 45/60)$ km. = 3.75 km.

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Read more trains in same direction Based Quantitative Aptitude Questions and Answers

Question : 1

A train 'B' speeding with 100 kmph crosses another train C, running in the same direction, in 2 minutes. If the length of the train B and C be 150 metre and 250 metre respectively, what is the speed of the train C (in kmph)?

a) 88

b) 95

c) 110

d) 75

Answer: (a)

Let the speed of train C be x kmph.

Relative speed of B

= (100 – x ) kmph.

Time taken in crossing

= $\text"Length of both trains"/ \text"Relative speed"$

$2/60 = {({150 + 250}/1000)}/{100 – x}$

$1/30 = 2/{5(100 – x)}$

$1/6 = 2/{100 – x}$

100 – x = 12

x = 100 – 12 = 88 kmph.

Question : 2

Two trains of equal length are running on parallel lines in the same direction at the rate of 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is

a) 72 m

b) 80 m

c) 82 m

d) 50 m

Answer: (d)

Length of each train = x metre

Relative speed

= 46 – 36= 10 kmph

= $(10 × 5/18)$ m/sec = $25/9$ m/sec

Time taken in crossing

= $\text"Length of both trains"/ \text"Relativespeed"$

36 = ${2x}/{25/9}$

$2x = 36 × 25/9$ = 100

$x = 100/2$ = 50 metre

Question : 3

A thief is stopped by a policeman from a distance of 400 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 5 km/h and that of policeman as 9 km/h, how far the thief would have run, before he is over taken by the policeman ?

a) 600 metre

b) 500 metre

c) 300 metre

d) 400 metre

Answer: (b)

Distance between thief and policeman = 400 metre

Relative speed of policeman with respect to thief

= (9 – 5) kmph = 4 kmph

= $({4 × 5}/18)$ m./sec. = $10/9$ m./sec.

Time taken in overtaking the thief

= $(400/{10/9})$ second

= $({400 × 9}/10)$ second = 360 second

Distance covered by thief

= Speed × Time

= $(5 × 5 × 18/360)$ metre

= 500 metre

Question : 4

A goods train starts running from a place at 1 P.M. at the rate of 18 km/hour. Another goods train starts from the same place at 3 P.M. in the same direction and overtakes the first train at 9 P.M. The speed of the second train in km/hr is

a) 30

b) 15

c) 18

d) 24

Answer: (d)

Distance covered by the first goods train in 8 hours = Distance covered by the second goods train in 6 hours.

18 × 8 = 6 × x

$x = {18 × 8}/6 = 24$ kmph

Question : 5

Two trains 125 metres and 115 metres in length, are running towards each other on parallel lines, one at the rate of 33 km/ hr and the other at 39 km/hr. How much time (in seconds) will they take to pass each other from the moment they meet ?

a) 10

b) 12

c) 15

d) 8

Answer: (b)

Relative speed

= (33 + 39) kmph = 72 kmph

= $({72 × 5}/18)$ m/sec. = 20 m/sec.

Time taken in crossing

= $\text"Length of both trains"/ \text"Relative speed"$

= ${125 + 115}/20 = 240/20$

= 12 seconds

Question : 6

Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes, the slower train in 36 seconds. The length of each train is :

a) 50 m

b) 80 m

c) 72 m

d) 82 m

Answer: (a)

Let the length of each train be x metre.

Relative speed

= 46 – 36 = 10 kmph

= ${10 × 5}/18$ metre/second

= $25/9$ metre/second

${2x}/{25/9} = 36$

2x = ${36 × 25}/9 = 100$

x = 50 metre

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