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 : A train travelling at 48 km/hr crosses another train, having half its length and travelling in opposite direction at 42 km/hr, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the railway platform is

(a) 300 m

(b) 350 m

(c) 400 m

(d) 200 m

The correct answers to the above question in:

Answer: (c)

Let the length of the train travelling at 48 kmph be x metres.

Let the length of the platform be y metres.

Relative speed of train

= (48 + 42) kmph

= ${90 × 5}/18$ m./sec. = 25 m./sec.

and 48 kmph = ${48 × 5}/18 = 40/3$ m./sec.

According to the question,

${x + {x/2}}/25$ = 12

${3x}/{2 × 25}$ =12

3x = 2 × 12 × 25 = 600

x = 200 m.

Also, ${200 + y}/{40/3}$ = 45

600 + 3y = 40 × 45

3y = 1800 - 600 = 1200

y = $1200/3$ = 400 m.

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

Question : 1

P and Q starting simultaneously from two different places proceed towards each other at a speed of 20 km/hour and 30 km/hour respectively. By the time they meet each other. Q has covered 36 km more than that of P. The distance (in km.) between the two places is

a) 162

b) 180

c) 108

d) 144

Answer: (b)

Let P and Q meet after t hours.

Distance = speed × time

According to the question,

30t - 20t = 36

10t = 36 ⇒ t = $36/10$ = 3.6 hours

Distance between P and Q

= 30t + 20t

= 50t = (50 × 3.6) km. = 180 km.

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 = 30, b = 20, d = 36

Required distance

= $({a + b}/{a - b}) × d$

= $({30 + 20}/{30 - 20}) ×$ 36

= $50/10 × 36$ = 180 km

Question : 2

Two trains start at the same time from Aligarh and Delhi and proceed towards each other at the rate of 14 km and 21 km per hour respectively. When they meet, it is found that one train has travelled 70 km more than the other. The distance between two stations is

a) 210 km

b) 300 km

c) 140 km

d) 350 km

Answer: (d)

Let the trains meet each other after t hours.

Distance = Speed × Time

According to the question,

21t - 14t = 70

7t = 70 ⇒ t = $70/7$ = 10 hours

Required distance

= 21t + 14t = 35t = 35 × 10 = 350 km.

Using Rule 13,

Here, a = 21, b = 14, d = 70

Required distance

= $({a + b}/{a - b}) × d$

= $({21 + 14}/{21 - 14}) × 70$

= $35/7 × 70$ = 350 km.

Question : 3

Two trains of lengths 150m and 180m respectively are running in opposite directions on parallel tracks. If their speeds be 50 km/ hr and 58 km/hr respectively, in what time will they cross each other?

a) 15 seconds

b) 30 seconds

c) 11 seconds

d) 22 seconds

Answer: (c)

Using Rule 3,

Relative speed = (50 + 58) kmph

= $(108 × 5/18)$ m/sec. = 30 m/sec

Required time

= $\text"Total length of trains"/ \text"Relative speed"$

= $({150 +180}/30)$ seconds

= $(330/30)$ seconds = 11 seconds

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GET trains PRACTICE TEST EXERCISES

Model 1 Train Vs Train in same direction

Model 2 Train Vs Train in opposite direction

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