Model 2 Train Vs Train in opposite 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 stations A and B and travel towards each other at speed of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is :

(a) 1200 km

(b) 1320 km

(c) 1440 km

(d) 990 km

The correct answers to the above question in:

Answer: (b)

Let train A start from station A and B from station B.

Let the trains A and B meet after t hours.

Distance covered by train A in t hours = 50t

Distance covered by train B in t hours = 60t km

According to the question,

60t - 50t = 120

t = $120/10$ = 12 hours.

Distance AB = 50 × 12 + 60 × 12

= 600 + 720 = 1320 km

Using Rule 13,
From stations A and B, two trains start travelling towards each other at speeds a and b, respectively. When they meet each other, it was found that one train covers distance d more than that of another train. The distance between stations A and B is given as
$({a + b}/{a - b}) × d$

Here, a = 60, b = 50, d = 120

Distance between A and B = $({a + b}/{a - b}) × d$

= $({60 + 50}/{60 - 50}) × 120$

= $110/10 × 120$ = 1320 km

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

Question : 1

Two trains, one 160 m and the other 140 m long are running in opposite directions on parallel rails, the first at 77 km an hour and the other at 67 km an hour. How long will they take to cross each other?

a) 7$1/2$ seconds

b) 6 seconds

c) 10 seconds

d) 7 seconds

Answer: (a)

Using Rule 2,
Let 'a' metre long train is travelling with the speed 'x' m/s and 'b' metre long train is travelling with the speed 'y' m/s in the opposite direction on parallel path.Then, time taken by the trains to cross each other
=$({a + b}/{x - y})$ seconds.

If two trains be moving in opposite directions at rate u and v kmph respectively,

then their relative speed = (u + v) kmph.

Further, if their length be x and y km. then time taken to cross each other

= ${x + y}/{u + v}$ hours.

Here, Total length = 160 + 140 = 300m.

Relative speed = (77 + 67) kmph

= 144 kmph = 144 × $5/18$ m/s or 40 m/sec.

Time = $300/40 = 7{1}/2$ Seconds

Question : 2

Two trains of equal length, running in opposite directions, pass a pole in 18 and 12 seconds. The trains will cross each other in

a) 15.5 seconds

b) 18.8 seconds

c) 20.2 seconds

d) 14.4 seconds

Answer: (d)

Using Rule 3,

Let the length of each train be x metre.

Speed of first train = $x/18$ m/sec

Speed of second train = $x/12$ m/sec

When both trains cross each other, time taken

= ${2x}/{x/18 + x/12}$

= ${2x}/{{2x + 3x}/36} = {2x × 36}/{5x}$

= $72/5$ = 14.4 seconds

Question : 3

Two trains start from station A and B and travel towards each other at speed of 16 miles/ hour and 21 miles/ hour respectively. At the time of their meeting, the second train has travelled 60 miles more than the first. The distance between A and B (in miles) is :

a) 496

b) 333

c) 540

d) 444

Answer: (d)

Let the trains meet after t hours

Then, 21t - 16t = 60

5t = 60 ⇒ t = 12 hours

Distance between A and B

= (16 + 21) × 12

= 37 × 12 = 444 miles

Using Rule 13,
From stations A and B, two trains start travelling towards each other at speeds a and b, respectively. When they meet each other, it was found that one train covers distance d more than that of another train. The distance between stations A and B is given as
$({a + b}/{a - b}) × d$

Here, a = 21, b = 16, d = 60

Distance between A and B

= $({a + b}/{a - b}) × d$

= $({21 + 16}/{21 - 16}) × 60$

= $37/5 × 60$ = 37 × 12 = 444 miles

Question : 4

Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is

a) 120 km/hr

b) 140 km/hr

c) 150 km/hr

d) 100 km/hr

Answer: (a)

Let the speed of second train be x m/s.

80 km/h = ${80 × 5}/18$ m/s

According to the question

$1000/{x + {80 × 5}/18}$ = 18

1000 = 18x + 400

x = $600/18$ m/s

= $600/18 × 18/5$ km/h = 120 km/h

Question : 5

Two trains start at the same time from A and B and proceed toward each other at the speed of 75 km/hr and 50 km/hr respectively. When both meet at a point in between, one train was found to have travelled 175 km more than the other. Find the distance between A and B.

a) 785 km.

b) 758 km.

c) 857 km.

d) 875 km.

Answer: (d)

Let the trains meet after t hours.

Distance = Speed × Time

According to the question,

75t - 50t = 175

25t = 175 ⇒ t = $175/25$ = 7 hours

Distance between A and B

= 75t + 50t = 125t

= 125 × 7 = 875 km.

Using Rule 13,

Here, a = 75, b = 50, d = 175

Required distance

= $({a + b}/{a - b}) × d$

= $({75 + 50}/{75 - 50}) × 175$

= $125/25 × 175$ = 125 × 7 = 875 km

Question : 6

Two trains of lengths 150m and 180m respectively are running in opposite directions on parallel tracks. If their speeds be 50 km/ hr and 58 km/hr respectively, in what time will they cross each other?

a) 15 seconds

b) 30 seconds

c) 11 seconds

d) 22 seconds

Answer: (c)

Using Rule 3,

Relative speed = (50 + 58) kmph

= $(108 × 5/18)$ m/sec. = 30 m/sec

Required time

= $\text"Total length of trains"/ \text"Relative speed"$

= $({150 +180}/30)$ seconds

= $(330/30)$ seconds = 11 seconds

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