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) 72 m
(b) 80 m
(c) 82 m
(d) 50 m
The correct answers to the above question in:
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
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Read more trains in same direction Based Quantitative Aptitude Questions and Answers
Question : 1
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
Question : 2
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 : 3
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 : 4
A train 'B' speeding with 100 kmph crosses another train C, running in the same direction, in 2 minutes. If the length of the train B and C be 150 metre and 250 metre respectively, what is the speed of the train C (in kmph)?
a) 88
b) 95
c) 110
d) 75
Answer »Answer: (a)
Let the speed of train C be x kmph.
Relative speed of B
= (100 – x ) kmph.
Time taken in crossing
= $\text"Length of both trains"/ \text"Relative speed"$
$2/60 = {({150 + 250}/1000)}/{100 – x}$
$1/30 = 2/{5(100 – x)}$
$1/6 = 2/{100 – x}$
100 – x = 12
x = 100 – 12 = 88 kmph.
Question : 5
Two trains start from a certain place on two parallel tracks in the same direction. The speed of the trains are 45 km/hr. and 40 km/ hr respectively. The distance between the two trains after 45 minutes will be
a) 2.75 km.
b) 3.7 km.
c) 3.75 km.
d) 2.5 km.
Answer »Answer: (c)
Relative speed = 45 – 40 = 5 kmph.
Gap between trains after 45 minutes
= $(5 × 45/60)$ km. = 3.75 km.
Question : 6
A goods train starts running from a place at 1 P.M. at the rate of 18 km/hour. Another goods train starts from the same place at 3 P.M. in the same direction and overtakes the first train at 9 P.M. The speed of the second train in km/hr is
a) 30
b) 15
c) 18
d) 24
Answer »Answer: (d)
Distance covered by the first goods train in 8 hours = Distance covered by the second goods train in 6 hours.
18 × 8 = 6 × x
$x = {18 × 8}/6 = 24$ kmph
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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