Model 1 Train Vs Train in same direction Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11 [SSC CPO S.I.2003]

A constable is 114 metres behind a thief. The constable runs 21 metres and the thief runs 15 metres in a minute. In what time will the constable catch the thief ?

a) 18 minutes

b) 17 minutes

c) 16 minutes

d) 19 minutes

Answer: (d)

Using Rule 1,
If a train crosses an electric pole, a sitting/standing man, km or mile stone etc. then distance = Length of train. Then,
Length of train = Speed × Time
And Time = $\text"Length of train"/\text"Speed"$ and
Speed = $\text"Length of train"/\text"Time"$

The gap of 114 metre will be filled at relative speed.

Required time = $(114/{21 – 15})$ minutes

= $114/6$ =19 minutes

Question : 12 [SSC CPO S.I.2005]

Two trains are running with speed 30 km/hr and 58 km/hr in the same direction. A man in the slower train passes the faster train in 18 seconds. The length (in metres) of the faster train is :

a) 100

b) 128

c) 140

d) 70

Answer: (c)

Relative speed

= (58 – 30) km/hr

= $(28 × 5/18)$ m/sec. = $70/9$ m/sec.

Length of train

= $70/9$ ×18 = 140 metres

Question : 13 [SSC CHSL 2013]

Two trains, of same length, are running on parallel tracks in the same direction with speed 60 km/hour and 90 km/hour respectively. The latter completely crosses the former in 30 seconds. The length of each train (in metres) is

a) 150

b) 100

c) 115

d) 125

Answer: (d)

When two trains cross each other, they cover distance equal to the sum of their length with relative speed.

Let length of each train = x metre

Relative speed

= 90 – 60 = 30 kmph

= $({30 × 5}/18)$ m/sec.

= $(25/3)$ m/sec.

${2x}/{25/3} = 30$

2x = ${30 × 25}/3$

2x = 250

x = 125 metres

Question : 14 [SSC CGL Prelim 2007]

Two trains travel in the same direction at the speed of 56 km/h and 29 km/h respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is

a) 80

b) 75

c) 120

d) 100

Answer: (b)

Relative speed

= 56 – 29 = 27 kmph

= $27 × 5/18 = 15/2$ m/sec

Distance covered in 10 seconds

= $15/2$ × 10 = 75 m

Hence, length of train = 75 m.

Question : 15 [SSC CGL Prelim 2000]

A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km./ hr and 11 km./hr respectively. What is the distance between them after 6 minutes ?

a) 190 m

b) 200 m

c) 150 m

d) 100 m

Answer: (d)

Using Rule 12,
If a train of length l m passes a bridge/platform of 'x' m in $t_1$ sec, then the time taken by the same train to cross another bridge/platform of length 'y' m is,
Time taken = $({l + y}/{l + x})t_1$

Relative speed of police

= 11 – 10 = 1 kmph

= $5/18$ m/sec

Distance decreased in 6 minutes

= $5/18$ × 6 × 60 = 100 m

Distance remained between them

= 200–100 = 100 m

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