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 men are standing on opposite ends of a bridge 1200 metres long. If they walk towards each other at the rate of 5m/minute and 10m/minute respectively, in how much time will they meet each other ?

(a) 80 minutes

(b) 85 minutes

(c) 90 minutes

(d) 60 minutes

The correct answers to the above question in:

Answer: (a)

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.

Men are walking in opposite directions.

Hence, they will cover the length of bridge at their relative speed.

Required time

= $1200/{(5 + 10)}$ = 80 minutes

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

Question : 1

Two trains 105 metres and 90 metres long, runs at the speed of 45 km/hr and 72 km/hr respectively, in opposite directions on parallel tracks. The time which they take to cross each other, is

a) 6 seconds

b) 7 seconds

c) 5 seconds

d) 8 seconds

Answer: (a)

Using Rule 3,

Length of both trains

= 105 + 90 = 195 m.

Relative speed

= (45 + 72) = 117 kmph

= 117 × $5/18$ or $65/2$ m/sec.

Time taken = $195/{65/2}$

= ${195 × 2}/65$ = 6 seconds

Question : 2

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: (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 : 3

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: (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 : 4

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.

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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

Model 3 Train Vs Bridge/Platform

Model 4 Train Vs Pole/Signal Post/Man

Model 5 Train Vs Both platform and a man/a pole

Model 6 Change in speed Vs Change with time travel
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