Model 1 Train Vs Train in same direction Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 6 EXERCISES

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The following question based on trains topic of quantitative aptitude

Questions : 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

The correct answers to the above question in:

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

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

Question : 1

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 : 2

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 : 3

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 : 4

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

Question : 5

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 : 6

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

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GET trains PRACTICE TEST EXERCISES

Model 1 Train Vs Train in same direction

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