Model 1 Train Vs Train in same direction Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on trains topic of quantitative aptitude
(a) 27 m
(b) 27$7/9$ m
(c) 23 m
(d) 23 4$2/9$ m
The correct answers to the above question in:
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
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Read more trains in same direction Based Quantitative Aptitude Questions and Answers
Question : 1
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 »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 × TimeAnd Time = $\text"Length of train"/\text"Speed"$ andSpeed = $\text"Length of train"/\text"Time"$
The gap of 114 metre will be filled at relative speed.
Required time = $(114/{21 – 15})$ minutes
= $114/6$ =19 minutes
Question : 2
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 »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 : 3
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 »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 : 4
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 »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 : 5
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 »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 : 6
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 »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
trains Shortcuts and Techniques with Examples
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Model 1 Train Vs Train in same direction
Defination & Shortcuts … -
Model 2 Train Vs Train in opposite direction
Defination & Shortcuts … -
Model 3 Train Vs Bridge/Platform
Defination & Shortcuts … -
Model 4 Train Vs Pole/Signal Post/Man
Defination & Shortcuts … -
Model 5 Train Vs Both platform and a man/a pole
Defination & Shortcuts … -
Model 6 Change in speed Vs Change with time travel
Defination & Shortcuts …
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