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 : 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

The correct answers to the above question in:

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.

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

Question : 1

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 : 2

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 : 3

A bus moving at a speed of 45 km/hr overtakes a truck 150 metres ahead going in the same direction in 30 seconds. The speed of the truck is

a) 24 km/hr

b) 25 km/hr

c) 28 km/hr

d) 27 km/hr

Answer: (d)

Let the speed of the truck be x kmph

Relative speed of the bus

= (45 – x) kmph

Time = $\text"Distance"/ \text"Relativespeed"$

$30/{60 × 60} = {150/1000}/({45 – x})$

$1/120 = 15/{100(45 – x)}$

$1/6 = 3/({45 – x})$

(45 – x ) = 18

x = 45 – 18 = 27 kmph

Question : 4

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.

Answer: (c)

Relative speed = 45 – 40 = 5 kmph.

Gap between trains after 45 minutes

= $(5 × 45/60)$ km. = 3.75 km.

Question : 5

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 : 6

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

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