Test: Problems On Trains- 2 - CUET MCQ

# Test: Problems On Trains- 2 - CUET MCQ

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## 10 Questions MCQ Test General Test Preparation for CUET - Test: Problems On Trains- 2

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Test: Problems On Trains- 2 - Question 1

### 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?

Test: Problems On Trains- 2 - Question 2

### 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

Detailed Solution for Test: Problems On Trains- 2 - Question 2

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

Test: Problems On Trains- 2 - Question 3

### 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

Detailed Solution for Test: Problems On Trains- 2 - Question 3

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

Test: Problems On Trains- 2 - Question 4

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?

Detailed Solution for Test: Problems On Trains- 2 - Question 4

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

Test: Problems On Trains- 2 - Question 5

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?

Detailed Solution for Test: Problems On Trains- 2 - Question 5

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.

Test: Problems On Trains- 2 - Question 6

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?

Detailed Solution for Test: Problems On Trains- 2 - Question 6

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

Test: Problems On Trains- 2 - Question 7

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?

Detailed Solution for Test: Problems On Trains- 2 - Question 7

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.

Test: Problems On Trains- 2 - Question 8

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?

Detailed Solution for Test: Problems On Trains- 2 - Question 8

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.

Test: Problems On Trains- 2 - Question 9

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

Detailed Solution for Test: Problems On Trains- 2 - Question 9

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

Test: Problems On Trains- 2 - Question 10

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

Detailed Solution for Test: Problems On Trains- 2 - Question 10

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

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