Solutions for Problems on trains

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?

A. 190 metres

B. 160 metres

C. 200 metres

D. 120 metres

Here is the answer and explanation

Answer : Option C

Explanation :

Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s

Time taken to cross, t = 18 s

Distance Covered, d = vt = (400/36)× 18 = 200 m

Distance covered is equal to the length of the train = 200 m



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

A. 270 m

B. 245 m

C. 235 m

D. 220 m


Here is the answer and explanation

Answer : Option B

Explanation :

Assume the length of the bridge = x meter

Total distance covered = 130+x meter

total time taken = 30s

speed = Total distance covered /total time taken = (130+x)/30 m/s

=> 45 × (10/36) = (130+x)/30

=> 45 × 10 × 30 /36 = 130+x

=> 45 × 10 × 10 / 12 = 130+x

=> 15 × 10 × 10 / 4 = 130+x

=> 15 × 25 = 130+x = 375

=> x = 375-130 =245





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.

A. 182 km/hr

B. 180 km/hr

C. 152 km/hr

D. 169 km/hr


Here is the answer and explanation

Answer : Option A

Explanation :

Length of the train, l = 150m

Speed of the man , Vm= 2 km/hr

Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr

Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)

=> 180 = Vt - 2

=> Vt = 180 + 2 = 182 km/hr





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?

A. 120 sec

B. 99 s

C. 89 s

D. 80 s


Here is the answer and explanation

Answer : Option C

Explanation :

v = 240/24 (where v is the speed of the train) = 10 m/s

t = (240+650)/10 = 89 seconds





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?

A. 38 sec

B. 35 s

C. 44 sec

D. 40 s


Here is the answer and explanation

Answer : Option D

Explanation :

Speed = 45 km/hr = 45×(10/36) m/s

= 150/12 = 50/4 = 25/2 m/s

Total distance = length of the train + length of the platform

= 360 + 140 = 500 meter

Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds



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?

A. Insufficient data

B. 3 : 1

C. 1 : 3

D. 3 : 2


Here is the answer and explanation

Answer : Option D

Explanation :

Let the speed of the trains be x and y respectively

length of train1 = 27x

length of train2 = 17y


Relative speed= x+ y

Time taken to cross each other = 23 s

=> (27x + 17 y)/(x+y) = 23

=> (27x + 17 y)/ = 23(x+y)

=> 4x = 6y

=> x/y = 6/4 = 3/2



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?

A. 46

B. 36

C. 18

D. 22


Here is the answer and explanation

Answer : Option B

Explanation :

Distance to be covered = 240+ 120 = 360 m

Relative speed = 36 km/hr = 36×10/36 = 10 m/s

Time = distance/speed = 360/10 = 36 seconds



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?

A. 88

B. 70

C. 62

D. 50


Here is the answer and explanation

Answer : Option D

Explanation :

Assume the length of each train = x

Total distance covered for overtaking the slower train = x+x = 2x

Relative speed = 46-36 = 10km/hr = (10×10)/36 = 100/36 m/s

Time = 36 seconds

2x/ (100/36) = 36

=> (2x × 36 )/100 = 36

=> x = 50 meter



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

A. 10.8 s

B. 12 s

C. 9.8 s

D. 8 s


Here is the answer and explanation

Answer : Option A

Explanation :

Distance = 140+160 = 300 m

Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s

Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s



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

A. 56

B. 48

C. 47

D. 26

Here is the answer and explanation

Answer : Option B

Explanation :

Relative speed = 60+90 = 150 km/hr (Since both trains are moving in opposite directions)

Total distance = 1.1+.9 = 2km

Time = 2/150 hr = 1//75 hr = 3600/75 seconds = 1200/25 = 240/5 = 48 seconds