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 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

The correct answers to the above question in:

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

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

Question : 1

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 : 2

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 : 3

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 : 4

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.

Question : 5

Two trains 140 m and 160 m long run at the speed of 60 km/ hour and 40 km/hour respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is :

a) 10.8 sec.

b) 9 sec.

c) 9.6 sec.

d) 10 sec.

Answer: (a)

Using Rule 3,

Total length of trains

= 140 + 160 = 300 m.

Relative speed

= 60 + 40 = 100 kmph

= 100 × $5/18$ m/sec. or $250/9$ m/sec.

Time taken to cross each other

= $300/{250/9} = {300 × 9}/250 = 10.8$ sec.

Question : 6

Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction ?

a) 15

b) 12

c) 10

d) 16

Answer: (b)

Using Rule 3,

When a train crosses a telegraph post, it covers its own length.

Speed of first train

= $120/10$ = 12 m/sec.

Speed of second train

= $120/15$ = 8 m/sec.

Relative speed

= 12 + 8 = 20 m/sec.

Required time

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

= ${2 × 120}/20$ = 12 seconds.

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