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

Question : 6 [SSC CGL Tier-II 2014]

Two trains of equal length are running on parallel lines in the same direction at the rate of 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is

a) 72 m

b) 80 m

c) 82 m

d) 50 m

Answer: (d)

Length of each train = x metre

Relative speed

= 46 – 36= 10 kmph

= $(10 × 5/18)$ m/sec = $25/9$ m/sec

Time taken in crossing

= $\text"Length of both trains"/ \text"Relativespeed"$

36 = ${2x}/{25/9}$

$2x = 36 × 25/9$ = 100

$x = 100/2$ = 50 metre

Question : 7 [SSC CHSL Tier-I 2017]

A thief is stopped by a policeman from a distance of 400 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 5 km/h and that of policeman as 9 km/h, how far the thief would have run, before he is over taken by the policeman ?

a) 600 metre

b) 500 metre

c) 300 metre

d) 400 metre

Answer: (b)

Distance between thief and policeman = 400 metre

Relative speed of policeman with respect to thief

= (9 – 5) kmph = 4 kmph

= $({4 × 5}/18)$ m./sec. = $10/9$ m./sec.

Time taken in overtaking the thief

= $(400/{10/9})$ second

= $({400 × 9}/10)$ second = 360 second

Distance covered by thief

= Speed × Time

= $(5 × 5 × 18/360)$ metre

= 500 metre

Question : 8 [SSC DEO 2008]

A bus moving at a speed of 45 km/hr overtakes a truck 150 metres ahead going in the same direction in 30 seconds. The speed of the truck is

a) 24 km/hr

b) 25 km/hr

c) 28 km/hr

d) 27 km/hr

Answer: (d)

Let the speed of the truck be x kmph

Relative speed of the bus

= (45 – x) kmph

Time = $\text"Distance"/ \text"Relativespeed"$

$30/{60 × 60} = {150/1000}/({45 – x})$

$1/120 = 15/{100(45 – x)}$

$1/6 = 3/({45 – x})$

(45 – x ) = 18

x = 45 – 18 = 27 kmph

Question : 9 [SSC CPO S.I.2004]

A constable follows a thief who is 200 m ahead of the constable. If the constable and the thief run at speed of 8 km/hour and 7 km/hour respectively, the constable would catch the thief in

a) 12 minutes

b) 15 minutes

c) 20 minutes

d) 10 minutes

Answer: (a)

The constable and thief are running in the same direction

Their relative speed

= 8 – 7 = 1km.

= 1 × $5/18$ m/sec.

∴ Required time = $200/{5/18}$

= ${200 × 18}/5$ = 720 sec

= $720/60$ minutes = 12 minutes

Question : 10 [SSC CGL Tier-II 2013]

Two trains are running 40 km/hr and 20 km/hr respectively in the same direction. The fast train completely passes a man sitting in the slow train in 5 seconds. The length of the fast train is

a) 27 m

b) 27$7/9$ m

c) 23 m

d) 23 4$2/9$ m

Answer: (b)

Relative speed

= 40 – 20 = 20 km/hour = ${20 × 5}/18$ m/sec.

Length of the faster train

= ${20 × 5}/18 × 5$ metres

= $250/9 = 27{7}/9$ metres

IMPORTANT quantitative aptitude EXERCISES

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