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) 15
(b) 12
(c) 10
(d) 16
The correct answers to the above question in:
Answer: (b)
Using Rule 3,
When a train crosses a telegraph post, it covers its own length.
Speed of first train
= $120/10$ = 12 m/sec.
Speed of second train
= $120/15$ = 8 m/sec.
Relative speed
= 12 + 8 = 20 m/sec.
Required time
= $\text"Total length of trains"/ \text"Relative speed"$
= ${2 × 120}/20$ = 12 seconds.
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Read more trains in opposite direction Based Quantitative Aptitude Questions and Answers
Question : 1
Two trains 140 m and 160 m long run at the speed of 60 km/ hour and 40 km/hour respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is :
a) 10.8 sec.
b) 9 sec.
c) 9.6 sec.
d) 10 sec.
Answer »Answer: (a)
Using Rule 3,
Total length of trains
= 140 + 160 = 300 m.
Relative speed
= 60 + 40 = 100 kmph
= 100 × $5/18$ m/sec. or $250/9$ m/sec.
Time taken to cross each other
= $300/{250/9} = {300 × 9}/250 = 10.8$ sec.
Question : 2
A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction, takes 4 seconds. The time taken by the trains to pass each other will be
a) 3$3/7$ seconds
b) 4$3/7$ seconds
c) 5$3/7$ seconds
d) 2$3/7$ seconds
Answer »Answer: (a)
Let the length of each train be x metres
Then, Speed of first train = $x/3$ m/sec
Speed of second train = $x/4$ m/sec
They are moving in opposite directions
Relaive speed = $x/3 + x/4$
= ${4x + 3x}/12 = {7x}/12$ m/sec.
Total length = x + x = 2 x m.
Time taken = ${2x}/{{7x}/12}$
= $24/7 = 3{3}/7$ sec.
Question : 3
Two trains 150 m and 120 m long respectively moving from opposite directions cross each other in 10 secs. If the speed of the second train is 43.2 km/hr, then the speed of the first train is
a) 50 km/hr
b) 52 km/hr
c) 51 km/hr
d) 54 km/hr
Answer »Answer: (d)
Using Rule 3,
Speed of second train = 43.2 kmph
= ${43.2 × 5}/18$ m/sec. or 12 m/sec.
Let the speed of first train be x m per second, then
${150 + 120}/{x + 12}$ = 10
27 = + x 12
x = 15 m/s
= 15 × $18/5$ kmph = 54 kmph
Question : 4
Two trains, each of length 125 metre, are running in parallel tracks in opposite directions. One train is running at a speed 65 km/hour and they cross each other in 6 seconds. The speed of the other train is
a) 85 km/hour
b) 95 km/hour
c) 105 km/hour
d) 75 km/hour
Answer »Answer: (a)
Using Rule 3,
Total length of both trains = 250 metres
Let speed of second train =x kmph
Relative speed = (65 + x) kmph
= (65 + x) × $5/18$ m/sec
Time
= $\text"Sumof length of trains"/ \text"Relative speed"$
6 = $250/{(65 + x) × 5/18$
$6 × 5/18 × (65 + x)$ = 250
65 + x = ${250 × 3}/5$
65 + x = 150
x = 150 - 65 = 85 kmph
Question : 5
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 : 6
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
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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