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 is moving at a speed of 80 km/h and covers a certain distance in 4.5 hours. The speed of the train to cover the same distance in 4 hours is

(a) 70 km/h

(b) 85 km/h

(c) 90 km/h

(d) 100 km/h

The correct answers to the above question in:

Answer: (c)

Distance = Speed × Time

= 80 × 4.5 = 360 km

∴ Required speed = $360/4$ = 90 kmph.

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

Question : 1

A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km/hr, at what speed is the first train moving ?

a) 50 km/hr.

b) 55 km/hr.

c) 25 km/hr.

d) 85 km/hr.

Answer: (d)

Suppose the speed of first train be x kmph

Speed of second train

= 30 kmph = ${30 × 1000}/60$

500 m per min.

According to question

$\text"Total Distance"/\text"Relativespeed"$

= $({66 + 88})/{x – 500} = 0.168$

$154/{x – 500} = 0.168$

0.168x – 84 = 154

0.168x = 238

$x = 238/0.168$

$({238 × 1000}/168)$m per minute

= ${238 × 1000}/168 × 3/50$ kmph = 85 kmph

Question : 2

Two trains, 80 metres and 120 metres long, are running at the speed of 25 km/hr and 35 km/hr respectively in the same direction on parallel tracks. How many seconds will they take to pass each other ?

a) 64

b) 70

c) 72

d) 48

Answer: (c)

Relative speed

= 35 – 25 = 10 kmph

= ${10 × 5}/18$ m/sec.

Total length = 80 + 120 = 200 metres

Required time

= $\text"Sum of the length of trains"/ \text"Relative speed"$

= $200/{{10 × 5}/18} = {200 × 18}/{10 × 5}$

= 72 seconds

Question : 3

A passenger train running at the speed of 80 kms./hr leaves the railway station 6 hours after a goods train leaves and overtakes it in 4 hours. What is the speed of the goods train?

a) 50 kmph

b) 45 kmph

c) 64 kmph

d) 32 kmph

Answer: (d)

Let the speed of goods train be x kmph.

Distance covered by goods train in 10 hour = distance covered by passenger train in 4 hours

10x = 80 × 4

$x = {80 × 4}/10$ = 32 kmph.

Question : 4

A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km./ hr and 11 km./hr respectively. What is the distance between them after 6 minutes ?

a) 190 m

b) 200 m

c) 150 m

d) 100 m

Answer: (d)

Using Rule 12,
If a train of length l m passes a bridge/platform of 'x' m in $t_1$ sec, then the time taken by the same train to cross another bridge/platform of length 'y' m is,
Time taken = $({l + y}/{l + x})t_1$

Relative speed of police

= 11 – 10 = 1 kmph

= $5/18$ m/sec

Distance decreased in 6 minutes

= $5/18$ × 6 × 60 = 100 m

Distance remained between them

= 200–100 = 100 m

Question : 5

Two trains travel in the same direction at the speed of 56 km/h and 29 km/h respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is

a) 80

b) 75

c) 120

d) 100

Answer: (b)

Relative speed

= 56 – 29 = 27 kmph

= $27 × 5/18 = 15/2$ m/sec

Distance covered in 10 seconds

= $15/2$ × 10 = 75 m

Hence, length of train = 75 m.

Question : 6

Two trains, of same length, are running on parallel tracks in the same direction with speed 60 km/hour and 90 km/hour respectively. The latter completely crosses the former in 30 seconds. The length of each train (in metres) is

a) 150

b) 100

c) 115

d) 125

Answer: (d)

When two trains cross each other, they cover distance equal to the sum of their length with relative speed.

Let length of each train = x metre

Relative speed

= 90 – 60 = 30 kmph

= $({30 × 5}/18)$ m/sec.

= $(25/3)$ m/sec.

${2x}/{25/3} = 30$

2x = ${30 × 25}/3$

2x = 250

x = 125 metres

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