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# Problems on Trains Questions

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Choose the correct option.

A 120 m long train is running at 72 Kmph. How much time will it take to cross a man standing on the platform?

A6 sec

B2.5 sec

C5 sec

D12 sec

Answer: Option A

Explanation:

Formula Used: Time = ( Distance / Speed)

As all the option given in sec., so convert the train speed (Kmph) in to mps multiply by 5/18

speed (mps) = 72 * 5/18 = 20 mps

Time = (120 / 20) sec = 6 sec

Time take by Train = 6 Sec.

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A train running at speed of 126 Kmph. What will be the length of train if it cross a tree in 5 sec.

A190 meters

B180 meters

C143 meters

D175 meters

ENone of these

Answer: Option D

Explanation:

Formula Used: Distance = (Speed * Time)
convert the train speed (Kmph) in to mps multiply by 5/18
speed (mps) = 126 * 5/18 = 35 mps
length = ( 35 * 5 ) meter
= 175 meter

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320m long train is running at 72 Kmph. how much time it will take to cross a platform of 180m long?

A20 sec

B30 sec

C25 sec

D27 sec

Answer: Option C

Explanation:

Total Length = Platform Length + Train Length
So Total Length = 500m

convert the train speed (Kmph) in to mps multiply by 5/18
speed (mps) = 72 * 5/18 = 20mps
Formula Used: Time = Distance/Speed
Time = (500 / 20 ) sec
= 25 sec

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A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 19 and 20 seconds respectively. The length of the train is:

A245 m

B211.1 m

C210 m

D213 m

Answer: Option B

Explanation:

Convert the persons Speed in m/sec
2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.
4 kmph = (4 x 5/18 m/sec = 10/9 m/sec.

Let the length of the train be x meters and its speed by y m/sec.
Relative speed in respect to both person (y - 5/9) and (y - 10/9)

Formula Used: Time = Distance / speed
so x / (y - 5/9) = 19 ---- (1)
and x / (y - 10/9) = 20 ---- (2)
9x = 19 (9y - 5) ----- (1)
9x = 20 (9y - 10) ------(2)
find the value of x and y
19 (9y - 5) = 20(9y - 10)
171 y - 95 = 180 y -200 => 9y = 105 => y = 105/9 = 35/3

Now find the value fo x by above any equations
9x = 171 *35/3 - 95 = 57 *35 - 95
9x = 1900 => x = 211.1 meter

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A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. If both the persons are walking in the same direction as the train? So What is the speed of the train ?

A96 km/hr

B51 km/hr

C81 km/hr

D76 km/hr

Answer: Option C

Explanation:

Convert the Speed in m/sec
so 4.5 km/hr = ( 4.5 x 5/18 ) m/sec = 5/4 m/sec = 1.25 m/sec,
and 5.4 km/hr = ( 5.4 x 5/18 ) m/sec = 3/2 m/sec = 1.5 m/sec.

Here assume the speed of the train as x m/sec.
so relative will be (x-1.25) and (x - 1.5)

(x - 1.25) x 8.4 = (x - 1.5) x 8.5

=> 8.4x - 10.5 = 8.5x - 12.75

=> 0.1x = 2.25
=> x = 22.5 m/s
As options are given in km/hr so convert the speed mps to kmph
So Speed of the train = ( 22.5 x 18/5 ) km/hr = 81 km/hr.

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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

Answer: Option C

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

Answer: Option B

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

Answer: Option B

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

Answer: Option C

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

Answer: Option C

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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