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) 3$3/7$ seconds
(b) 4$3/7$ seconds
(c) 5$3/7$ seconds
(d) 2$3/7$ seconds
The correct answers to the above question in:
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.
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Read more trains in opposite direction Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
A train running at the speed of 84 km/hr passes a man walking in opposite direction at the speed of 6 km/hr in 4 seconds. What is the length of train (in metre) ?
a) 120
b) 100
c) 90
d) 150
Answer »Answer: (b)
Using Rule 6,Let 'a' metre long train is running with the speed 'x' m/s. A man is running in the opposite direction of train with the speed of 'y' m/s. Then, time taken by the train to cross the man = $(a/{(x + y)})$seconds.
Relative speed
= (84 + 6) = 90 kmph
= $(90 × 5/18)$ m/sec. = 25 m/sec.
Length of train
= Relative speed × Time
= 25 × 4 = 100 metre
Question : 3
Two trains of length 70 m and 80 m are running at speed of 68 km/hr and 40 km/hr respectively on parallel tracks in opposite directions. In how many seconds will they pass each other ?
a) 8 sec
b) 5 sec
c) 3 sec
d) 10 sec
Answer »Answer: (b)
Using Rule 3,
Relative speed
= (68 + 40) kmph = 108 kmph
= $({108 × 5}/18)$ m/s or 30 m/s
Required time
= $\text"Sum of the lengths of both trains"/ \text"Relative speed"$
= $({70 + 80}/30)$ second = 5 seconds
Question : 4
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 : 5
Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction ?
a) 15
b) 12
c) 10
d) 16
Answer »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.
Question : 6
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
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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