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QUESTION: 1

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?

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: 2

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?

Solution:

Speed = 240/24 m/sec

= 10m/sec

∴ Requiredtime = (240+650)/10sec.

= 89sec.

QUESTION: 3

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

Solution:

45*(5/18) = 12.5

=>(130+x)/12.5 = 30

=>(130+x) = 375

=> x = 375 - 130

=>x = 245

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

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

Solution:

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

Solution:

When a moving train with a velocity V_{1} passes a man with velocity V_{2}, then,

Relative velocity of train w.r.t man V= V_{1}-V_{2}

Velocity of the man V2 = 2 km/h = 2000/(60x60) = (5/9) m/s

Thus, V = V_{1} - (5/9)

Distance (d) = Time (t) x velocity (V)

d=150 m

t = 3 sec

V = V_{1}- (5/9)

Hence,

150 = 3 x [V_{1}- (5/9)]

50 = V_{1}- (5/9)

V_{1} = 50+ (5/9)

On simplification,

V_{1} = (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?

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 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

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: 9

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?

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: 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?

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.

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