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# Problems on Trains Questions

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Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

A2 :3

B6:7

C4 :3

D9 :16

Explanation:

Let's name both trains as A and B. Then,
Formula Used: _/(A's speed) : _/(B's speed) = _/b : _/a
?(A's speed) : ?(B's speed) = _/16 : _/9 = 4 : 3.

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A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A150 km/hr

B50 km/hr

C75 km/hr

D55 km/hr

Explanation:

Let's assume the speed of the train x km/hr.
so relative speed = (x - 5) km/hr. so speed (mps) = (x-5) * 5/18

Formula Used: Distance = Speed * Time
125 = (x-5) * 5/18 * 10 => 125 = (50x - 250 )/18
=> 125 * 18 = 50x -250
50x = 2500 => x = 50
x = 50 km/hr.

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

A2 : 3

B3: 2

C3 : 7

D3 : 4

Explanation:

Assume both train speeds as x m/sec and y m/sec respectively.

So Length of the first train = 27x meters,

and Length of the second train = 17y meters.
They cross each other in 23 sec.
Relative speed of train = (x + y) and total length = (27x + 17y)

Formula Used: Time = Distance / speed.
=> 23 = (27x + 17y)/(x + y)

27x + 17y = 23x + 23y

4x = 6y
So ratio of their speeds
=> x : y = 3 : 2

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A 240m long train is running at 90kmph. If it crossed the platform in 30sec, then find the length of the platform?

A500m

B490m

C510m

D550m

Explanation:

Train speed in (m/sec) = 90 * 5/18 = 25 m/sec
total Length = 25 * 30 m = 750 m

So Length of Platform= (Total Length - Length of the Train)
= (750 - 240)
= 510m

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Two trains running in opposite directions at 40kmph and 50kmph, cross each other in 30sec. The length of one train is 250m, then find the length of other one?

A520m

B510m

C500m

D490m

Explanation:

Relative Speed = ( 40 + 50 ) kmph = 90 kmph
= (90 * 5/18) m/sec = 25 m/sec
Distance covered = 25 * 30 m = 750 m

Length of second train = total length - Length of first train
= (750 - 250)m = 500m

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A train crosses a platform of 120m in 15sec, same train crosses another platform of length 180m in 18sec. then find the length of the train?

A180 m

B175 m

C185 m

D170 m

Explanation:

Let's assume Length of the train = x meters

(X + 120)/15 = (X + 180)/18

6X + 720 = 5X + 900

X = 180m

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A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

A400 m

B450 m

C560 m

D600 m

E600 m

Explanation:

Let's assume the length of the first train = x meters.

Then, the length of the second train = x /2 meters.

Relative speed = (48 + 42) kmph = ( 90 * 5/18 ) m/sec = 25 m/sec.

Therefore [x + (x/2)] /25 = 12
=> 3x /2 = 300 => x = 200.

Therefore Length of first train = 200 m.

Let's assume length of platform = y meters.
So total length = (200 + y) meters.

Speed of the first train = ( 48 * 5 /18 ) m/sec = 40/3 m/sec.

Therefore (200 + y) /(40/3) = 45 => (600 + 3y ) = 45 * 40

=> 600 + 3y = 1800

=> y = 400 m.
Platform length = 400 meters.

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A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

A48 km/hr

B54 km/hr

C66 km/hr

D82 km/hr

Explanation:

Let the speed of the second train = x km/hr.

So Relative speed = (x + 50) km/hr

= [ (x + 50) * 5/18 ] m/sec

= [ 250 + 5x ]/18 m/sec.

Distance covered = (108 + 112) = 220 m.

Therefore 220 = 6 * ( 250 + 5x)/18

=> 250 + 5x = 660
=> 5x = 660 - 250 => 5x = 410

=> x = 82 km/hr.
Second Train speed = 82 km/hr.

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A train travelling at a speed of 75 mph enters a tunnel 3 1/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

A2.5 min

B3 min

C3.2 min

D3.5 min

Explanation:

Total distance covered by train = ( 7/2 + 1/4 ) miles = 15/4 miles.

Therefore Time taken = ( 15/4) / 75 hrs = 1/20 hrs

= ( 1/20 x 60 ) min. = 3 min.

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A 300 meters long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

A320 m

B350 m

C650 m

Explanation:

Cross signal pole in 18 sec
so train Speed = ( 300 /18) m/sec = 50/3 m/sec.

Let the length of the platform = x meters.
Formula Used : speed = Distance / Time
so ( x + 300 ) /39 = 50/3

=> 3(x + 300) = 1950 => 3x + 900 = 1950

=> x = 350 m.

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