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

Question : 21 [SSC MTS 2013]

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 : 22 [SSC CHSL 2010]

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 : 23 [SSC GL Tier-I 2013]

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 : 24 [SSC CGL Tier-II 2015]

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 : 25 [SSC CPO S.I.2009]

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.

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