Model 2 Train Vs Train in opposite direction Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11 [SSC CGL Prelim 2003]

Two trains are running in opposite direction with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, the speed of each train (in km/hour) is

a) 10

b) 36

c) 18

d) 72

Answer: (b)

Using Rule 3,

Let the speed of each train be x kmph.

Their relative speed

= x + x = 2x kmph.

Time taken

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

= $12/{60 × 60} = {240 × {1/1000}}/{2x}$

= $1/300 = 120/{1000x}$

$x = {300 × 120}/1000$ = 36

The required speed = 36 kmph.

Question : 12 [SSC CHSL 2013]

Two trains, each of length 125 metre, are running in parallel tracks in opposite directions. One train is running at a speed 65 km/hour and they cross each other in 6 seconds. The speed of the other train is

a) 85 km/hour

b) 95 km/hour

c) 105 km/hour

d) 75 km/hour

Answer: (a)

Using Rule 3,

Total length of both trains = 250 metres

Let speed of second train =x kmph

Relative speed = (65 + x) kmph

= (65 + x) × $5/18$ m/sec

Time

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

6 = $250/{(65 + x) × 5/18$

$6 × 5/18 × (65 + x)$ = 250

65 + x = ${250 × 3}/5$

65 + x = 150

x = 150 - 65 = 85 kmph

Question : 13 [SSC CGL Prelim 2004]

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.

Question : 14 [SSC CGL Prelim 2004]

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 : 15 [SSC CPO S.I.2006]

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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