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

Questions : 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

The correct answers to the above question in:

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

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Read more trains in opposite direction Based Quantitative Aptitude Questions and Answers

Question : 1

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: (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

Question : 2

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: (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 : 3

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: (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 : 4

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: (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 : 5

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: (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 : 6

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: (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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