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, 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

The correct answers to the above question in:

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

Question : 1

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 : 2

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 : 3

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

Answer: (c)

Distance = Speed × Time

= 80 × 4.5 = 360 km

∴ Required speed = $360/4$ = 90 kmph.

Question : 4

Two trains are running with speed 30 km/hr and 58 km/hr in the same direction. A man in the slower train passes the faster train in 18 seconds. The length (in metres) of the faster train is :

a) 100

b) 128

c) 140

d) 70

Answer: (c)

Relative speed

= (58 – 30) km/hr

= $(28 × 5/18)$ m/sec. = $70/9$ m/sec.

Length of train

= $70/9$ ×18 = 140 metres

Question : 5

A constable is 114 metres behind a thief. The constable runs 21 metres and the thief runs 15 metres in a minute. In what time will the constable catch the thief ?

a) 18 minutes

b) 17 minutes

c) 16 minutes

d) 19 minutes

Answer: (d)

Using Rule 1,
If a train crosses an electric pole, a sitting/standing man, km or mile stone etc. then distance = Length of train. Then,
Length of train = Speed × Time
And Time = $\text"Length of train"/\text"Speed"$ and
Speed = $\text"Length of train"/\text"Time"$

The gap of 114 metre will be filled at relative speed.

Required time = $(114/{21 – 15})$ minutes

= $114/6$ =19 minutes

Question : 6

Two trains are running 40 km/hr and 20 km/hr respectively in the same direction. The fast train completely passes a man sitting in the slow train in 5 seconds. The length of the fast train is

a) 27 m

b) 27$7/9$ m

c) 23 m

d) 23 4$2/9$ m

Answer: (b)

Relative speed

= 40 – 20 = 20 km/hour = ${20 × 5}/18$ m/sec.

Length of the faster train

= ${20 × 5}/18 × 5$ metres

= $250/9 = 27{7}/9$ metres

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