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 : 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.

The correct answers to the above question in:

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.

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

Question : 1

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 : 2

Two trains of length 137 metre and 163 metre are running with speed of 42 km/hr and 48 km/hr respectively towards each other on parallel tracks. In how many seconds will they cross each other?

a) 24 sec

b) 12 sec

c) 10 sec

d) 30 sec

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

Question : 3

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: (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 : 4

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 : 5

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: (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 : 6

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

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