PROBLEMS ON TRAIN

 PROBLEMS ON TRAIN

Concepts 

• Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres. 

• Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres. 

• Two trains or objects are moving in the same direction at u m/s and v m/s speeds, then their relative speed = (u - v) m/s.

• Two trains or objects are moving in the opposite direction at u m/s and v m/s speeds, then their relative speed = (u + v) m/s.

• Two trains of lengths a & b metres are moving in same directions at u m/s and v m/s, then time taken to cross each other = (a + b) / ( u - v) second 

• Two trains of lengths a & b metres are moving in opposite directions at u m/s and v m/s, then time taken to cross each other = (a + b) / ( u + v) second 

• If two trains start at the same time from points A & B towards each other and after crossing they take a & b second in reaching B & A respectively,  then (A's speed) : (B's speed) = √b : √a 

• If two trains of same lengths are coming from same direction and cross a man in t₁ and t₂ seconds,  then time taken by both the trains to cross each other = 2 × (product of time)/(difference of time).

• If two trains of same lengths are coming from opposite direction and cross a man in t₁ and t₂ seconds,  then time taken by both the trains to cross each other = 2 × (product of time)/(sum of time).

• Conversation from km/hr to m/s :- 1 km/hr = 5/18 m/s.

• Conversation from m/s to km/hr :- 1 m/s = 18/5 km/hr.

Examples 

1. A train is moving at a speed of 132 km/hr. If the length of the train is 110 m, how long will it take to cross a railway platform 165 m long?

Solution:

Speed of train = 132 × 5/18 = 110/3 m/s

Distance = l + b = 110 + 165 = 275 m

Time taken = 275 ÷ 110/3 = 15/2 s.

2. A man is standing on a railway bridge which is 180 m long.  He finds that a train crosses the bridge in 20 s but himself in 8 s. Find the length of the train and its speed?

Solution:

Let the length of train be x metres. 

Train covers x metres in 8 s and (x + 180) m in 20 s.

Then, x/8 = (x + 180)/20 

On solving,  x = 120 m

Speed of train = 120/8 = 15 m/s.

3. A train 100 m long takes 6 s to cross a man walking at 5 kmph in a direction opposite to that of the train.  Find the speed of the train?

Solution:

Let speed of train = x

Speed of man = 5 kmph 

Relative speed of man and train = (x +5) × 5/18 m/s

According to question, 

     100/[(x + 5) × 5/18] = 6 , then x = 55 kmph 

4. A train without stoppage travels with an average speed of 72 km/hr and with stoppage, it travels with an average speed of 60 km/hr. For how many minutes does the train stop on an average per hour? 

Solution:

  More distance covered in one hour without stoppage = 72 - 60 = 12 km

Required time = (12/72) × 60 = 10 minutes 

Previous Years Questions 

1. A train is moving at 120 km/hr. The length of the train is 150 meters. How long it will take to cross a platform of length 100 meters ? (Ans. 7.5 second)

2. A train covers a distance of 10 km in 12 minutes.  If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance will be ----? (Ans. 13 minutes 20 seconds)

3. A train covers a distance of 225 km in 2.5 hr at a uniform speed.  The time taken, in hours, to cover a distance of 450 km at the same speed is -? (Ans. 5 hr.)

4. If a train maintains an average speed of 42 km/hr, it arrives at its destination at the time.  If however,  the average speed is 40 km/hr, it arrives 15 minutes late. Find the length of the journey? (Ans. 210 km)

5. A train goes from P to Q with a speed u km/hr, then from Q to R (QR = 2PQ) with a speed of 3u km/hr and returns from R to P with a speed of u/2 km/hr. What is the average speed in km/hr of train for the entire journey start from P and back to P? (Ans. 18u/23)

6. A train covers a certain distance in 45 minutes.  If its speed is reduced by 5 km/hr, it takes 3 minutes more to cover the same distance.  The distance in km is ----? (Ans. 60 km)

7. Two trains,  one from Howarah to Patna and the other from Patna to Howarah,  start simultaneously.  After they meet, the trains reach their destinations after 9 hrs and 16 hrs respectively.  The ratio of their speeds is -----? (Ans. 4 : 3)

8. Two trains running in opposite directions cross a man standing on the platform in 27s and 17s respectively  and they cross each other in 23s. The ratio of their speeds is :-------? (Ans.3 : 2)

9. A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is ----? (Ans.500)

10. Two goods train each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? (Ans. 48 sec)