# Arithmetic Aptitude :: Problems on Trains

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A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A120 metres

B180 metres

C324 metres

D150 metres

Explanation:

Length of the train = (Speed x Time) =50/3 x 9 m = 150 m.

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A 600m long train is running at 73 Kmph. How much time Train will take to cross an electric pole?

A29.58 sec

B28.58sec

C29 sec

D28sec

ENone of these

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) = 73 * 5/18
Time = 600 / (73 * 5/18)
= (600 * 18 )/(73 * 5) sec
= (10800 / 365)
Time take by Train = 29.58Sec

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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

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

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

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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Two trains 400m and 300m long run at the speeds of 50 kmph and 40kmph respectively in opposite Directions on parallel tracks. The time taken to cross each other?

A20 sec

B28 secs

C25 sec

D24 sec

ENone of these

Explanation:

Trains are running in opposite Direction:
So need to find Length of two Trains = 300m + 400m = 700m

and Total Speed = 40 Kmph + 50 Kmph (Opposite Direction)
= 90 Kmph
so speed (m/sec) = 90 * 5/18 m/sec = 25 m/sec
Formula Used: Time = Distance/Speed

Time = 700/ 25 sec
Time = 28 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

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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Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

A10 a.m.

B11 a.m.

C10 p.m.

D11 p.m.

Explanation:

Let they meet x hours after 7 a.m.

Distance covered by A in x hours = 20x km.

Distance covered by B in (x - 1) hours = 25(x - 1) km.

So Total Distance
=> 20x + 25(x - 1) = 110
=> 45x - 25 = 110 => 45x = 135
=> x = 3.
As They meet x hrs after 7 a.m. so they meet at 10 a.m.

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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

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 are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

A27 m

B33 m

C27 7/9 m

D23 4/9 m

Explanation:

As train are running in same direction
so Relative speed = (40 - 20) km/hr = 20 km/hr
= ( 20 x 5/18 ) m/sec = 50/9 m/sec.
Formula Used: Distance = Speed * Time
Now Length of Faster Train = ( 50/9 x 5 ) m = 250/9 m
= 27 7/9 m

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