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) 24 sec
(b) 12 sec
(c) 10 sec
(d) 30 sec
The correct answers to the above question in:
Answer: (b)
Using Rule 3,
Relative speed
= 42 + 48 = 90 kmph
= $({90 × 5}/18)$ m/s = 25 m/s
Sum of the length of both trains
= 137 + 163 = 300 metres
Required time = $300/25$ = 12 seconds
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Read more trains in opposite direction Based Quantitative Aptitude Questions and Answers
Question : 1
A train, 150m long, passes a pole in 15 seconds and another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train is
a) 48 km/hr
b) 52 km/hr
c) 54 km/hr
d) 45 km/hr
Answer »Answer: (c)
Using Rule 3,
Let the speed of the second train be x m/s
Speed of first train
= $150/15$ = 10 m/sec
Relative speed of trains
= (x + 10) m/s
Total distance covered
= 150 + 150 = 300 metre
Time taken = $300/{x + 10}$
$300/{x + 10}$ = 12
12x + 120 = 300
12x = 300 - 120 = 180
x = $180/12$ = 15 m/s
= ${15 × 18}/5$ or 54 kmph.
Question : 2
Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8 km/hour faster than the other, then speed of train from Q is
a) 10$5/6$ km/hour
b) 9$1/2$ km/hour
c) 8$1/2$ km/hour
d) 12$5/6$ km/hour
Answer »Answer: (b)
Speed of train starting from Q = x kmph
Speed of train starting from P = (x + 8) kmph
According to the question,
PR + RQ = PQ
(x + 8) × 6 + x × 6 = 162
[Distance = Speed × Time]
6x + 48 + 6x = 162
12x = 162 - 48 = 114
x = $114/12 = 19/2 = 9{1}/2$ kmph
Question : 3
Two towns A and B are 500 km. apart. A train starts at 8 AM from A towards B at a speed of 70 km/ hr. At 10 AM, another train starts from B towards A at a speed of 110 km/hr. When will the two trains meet ?
a) 12 Noon
b) 12.30 PM
c) 1.30 PM
d) 1 PM
Answer »Answer: (a)
Let two trains meet after t hours when the train from town A leaves at 8 AM.
Distance covered in t hours at 70 kmph
+ Distance covered in (t - 2) hours at 110 kmph = 500km
70t + 110 (t - 2) = 500
70t + 110t - 220 = 500
180 t = 500 + 220 = 720
t = $720/180$ = 4 hours
Hence, the trains will meet at 12 noon.
Question : 4
Two trains 108 m and 112 m in length are running towards each other on the parallel lines at a speed of 45 km/hr and 54 km/ hr respectively. To cross each other after they meet, it will take
a) 9 sec
b) 8 sec
c) 10 sec
d) 12 sec
Answer »Answer: (b)
Using Rule 3,
Relative speed
= 45 + 54 = 99 kmph
= $(99 × 5/18)$ m/sec. or $55/2$ m/sec.
Required time = ${108 + 112}/{55/2}$
= ${220 × 2}/55 = 8$ seconds
Question : 5
The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
a) 10 : 30 a.m.
b) 11 a.m.
c) 11 : 30 a.m.
d) 10 a.m.
Answer »Answer: (b)
Distance travelled by first train in one hour
= 60 × 1 = 60km
The given distance between two cities A and B is 330 km.
Therefore, distance between two train at 9 a.m.
= 330 - 60 = 270 km
Now, Relative speed of two trains
= 60 + 75 = 135 km/hr
Time of meeting of two trains
= $270/135$ = 2 hrs.
Therefore, both the trains will meet at
9 + 2 = 11 A.M.
Question : 6
Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur respectively. After passing each other they take 4 hours 48 minutes and 3 hours 20 minutes to reach Jaipur and Jodhpur respectively. If X is moving at 45 km/hr, the speed of Y is
a) 58 km/hr
b) 54 km/hr
c) 64.8 km/hr
d) 60 km/hr
Answer »Answer: (b)
Using Rule 11,Two trains A and B, run from stations X to Y and from Y to X with the speed '$S_A$' and '$S_B$' respectively. After meeting with each other. A reached at Y after '$t_A$' time and B reached at X after '$t_B$' time. Then Ratio of speeds of trains,$S_A/S_B = √{t_B/t_A}$
$\text"Speed of X"/\text"Speed of Y"$
= $√\text"Time taken by Y"/\text"Time taken by X"$
$45/y = √\text"3 hours 20 min"/\text"4 hours 48 min"$
$45/y = √\text"200 minutes"/\text"288 minutes" = 10/12$
10y = 12 × 45
$y = {12 × 45}/10$ = 54 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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