Model 2 Train Vs Train in opposite direction Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC SO 2006]

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 : 7 [SSC CPO S.I.2005]

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

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

Question : 8 [SSC CGL Prelim 2003]

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 : 9 [SSC CGL Prelim 2008]

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 : 10 [SSC MTS 2013]

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

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