Test: Problems On Trains- 2

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This mock test of Test: Problems On Trains- 2 for CAT helps you for every CAT entrance exam. This contains 10 Multiple Choice Questions for CAT Test: Problems On Trains- 2 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Problems On Trains- 2 quiz give you a good mix of easy questions and tough questions. CAT students definitely take this Test: Problems On Trains- 2 exercise for a better result in the exam. You can find other Test: Problems On Trains- 2 extra questions, long questions & short questions for CAT on EduRev as well by searching above.

QUESTION: 1

A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m?

A.
120 sec
B.
99 s
C.
89 s
D.
80 s

Solution:

Speed = 240/24 m/sec
= 10m/sec
∴ Requiredtime = (240+650)/10sec.
= 89sec.

QUESTION: 2

A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?

A.
46
B.
36
C.
18
D.
22

Solution:

Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.
= (36 x 5/18)m/sec
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.
Time taken = 360/10
= 36 sec.

QUESTION: 3

A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?

A.
190 metres
B.
160 metres
C.
200 metres
D.
120 metres

Solution:

QUESTION: 4

Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is

A.
10.8s
B.
12s
C.
9.8s
D.
8s

Solution:

Relative speed = (60+40)km/hr
= (100×5/18) m/sec
= (250/9) m/sec
Distance covered in crossing each other =(140+160)m
= 300m
Required time = Distance/Time
=> 300/(250/9)
= 300*(9/250)
= 54/5
= 10.8 sec

QUESTION: 5

A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is

A.
270 m
B.
245 m
C.
235 m
D.
220 m

Solution:

45*(5/18) = 12.5
=>(130+x)/12.5 = 30
=>(130+x) = 375
=> x = 375 - 130
=>x = 245

QUESTION: 6

A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train

A.
182 km/hr
B.
180 km/hr
C.
152 km/hr
D.
169 km/hr

Solution:

When a moving train with a velocity V₁ passes a man with velocity V₂, then,
Relative velocity of train w.r.t man V= V₁-V₂
Velocity of the man V2 = 2 km/h = 2000/(60x60) = (5/9) m/s
Thus, V = V₁ - (5/9)
Distance (d) = Time (t) x velocity (V)
d=150 m
t = 3 sec
V = V₁- (5/9)
Hence,
150 = 3 x [V₁- (5/9)]
50 = V₁- (5/9)
V₁ = 50+ (5/9)
On simplification,
V₁ = (455/9) m/s = (455/9)x(3600/1000) km/h= 182 km/h
Speed of the train= 182 km/h

QUESTION: 7

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

A.
88
B.
70
C.
62
D.
50

Solution:

Let the length of each train be x metres
Then, distance covered = 2x metres.
Relative speed =(46−36)km/hr
= [10 * 5/8 * 10]m/sec
= 25/9 m/sec
2x/36 = 25/9
x = 50
Length of each train is 50m.

QUESTION: 8

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?

A.
Insufficient data
B.
3 : 1
C.
1 : 3
D.
3 : 2

Solution:

Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
Length of the second train = 17y metres.
[because distance = speed*time]
(27x+17y)/(x+y) = 23
=> 27x + 17y = 23x + 23y
=> 4x = 6y
=> x/y = 6/4

QUESTION: 9

Two trains are moving in opposite directions with speed of 60 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds

A.
56
B.
48
C.
47
D.
26

Solution:

Relative speed (60+90)km/hr
= 150km/hr
= 150 × 5/18 m/sec
= 125/3 m/sec
Distance covered by the slower train to cross the faster train =(1.1+0.9)km
= 2km = 2000m
The time taken by the slower train to cross the faster train in second = distance/speed = 2000/(125/3)
= 16 * 3
= 48 sec

QUESTION: 10

A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?

A.
38 sec
B.
35 s
C.
44 sec
D.
40 s

Solution:

Formula For Converting From Km/hr to m/s:
Xkm/hr = X × 5/18m/s
Therefore, Speed = 45 × 5/18m/sec
= 252m/sec
Total Distance To Be covered = (360+140)m=500m
Formula for finding
Time = Distance/Speed
∴ Requiredtime = (500×20/25sec
= 40sec.