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
(a) 7$1/2$ seconds
(b) 6 seconds
(c) 10 seconds
(d) 7 seconds
The correct answers to the above question in:
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
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Read more trains in opposite direction Based Quantitative Aptitude Questions and Answers
Question : 1
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 »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 : 2
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 »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 : 3
Two trains are running in opposite direction with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, the speed of each train (in km/hour) is
a) 10
b) 36
c) 18
d) 72
Answer »Answer: (b)
Using Rule 3,
Let the speed of each train be x kmph.
Their relative speed
= x + x = 2x kmph.
Time taken
= $\text"Total length of trains"/\text"Relative Speed"$
= $12/{60 × 60} = {240 × {1/1000}}/{2x}$
= $1/300 = 120/{1000x}$
$x = {300 × 120}/1000$ = 36
The required speed = 36 kmph.
Question : 4
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 »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 : 5
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 »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 : 6
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 »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
trains Shortcuts and Techniques with Examples
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Model 1 Train Vs Train in same direction
Defination & Shortcuts … -
Model 2 Train Vs Train in opposite direction
Defination & Shortcuts … -
Model 3 Train Vs Bridge/Platform
Defination & Shortcuts … -
Model 4 Train Vs Pole/Signal Post/Man
Defination & Shortcuts … -
Model 5 Train Vs Both platform and a man/a pole
Defination & Shortcuts … -
Model 6 Change in speed Vs Change with time travel
Defination & Shortcuts …
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