Train solved Problems

Problems on Trains

1.  A train 100m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line?

Answer: 12 sec
Explanation:
Speed of the train = [ 30 * ( 5 / 18 ) ] m/sec [ ∴ ( a ) km/hr = ( a * ( 5 / 18 ) ) m/s ]
= ( 25 / 3 ) m/sec
Distance moved in passing the standing man = 100m
Required time taken = [ 100 / ( 25 / 3 ) ]
= [ 100 * ( 3 / 15 ) ]
= 12 sec.


2.  A train 150m long is running with a speed of 68kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?

Answer: 9 sec
Explanation:
Speed of the train relative to man = ( 68 - 8 )kmph
= 60 kmph
= [ 60 * ( 5 / 18 ) ] m/sec [ ∴ ( a ) km/hr = ( a * ( 5 / 18 ) ) ]
= [ ( 10 * 5 ) / 3 ]
= ( 50 / 3 )
Time taken by the train to cross the man = Time taken by it to cover 150 m at ( 50 / 3 ) m/sec
= [ ( 150 * 3 ) / 50 ]sec
= ( 3 * 3 )
= 9 sec.


3.  A 180m long train is running at 72 Kmph. If it crossed the platform in 20sec. then find the platform Length?

Answer: 220 m
Explanation:
Length = Speed * Time
Length = 72 km/hr * Time
Length = [ 72 * ( 5 / 18 ) ] * 20 [ ∴ ( x ) km/hr = ( x * ( 5 / 18 ) ) ]
= 20 * 20
Length = 400 m
Length of Platform = Length - Length of the Train
Length of Platform = 400 - 180
Length of Platform = 220 m.


4.  A train 137 metres and 163 metres in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmph. In what time will they be clear of each other from the moment they meet?

Answer: 12 seconds
Explanation:
Relative speeed of the trains = ( 42 + 48 ) kmph
= 90 kmph
= [ 90 * ( 5 / 18 ) ] m/sec
= 25 m/sec
Time taken by the trains to pass each other = ( 137 + 163 ) / 25
= 300 / 25
= 12 seconds.


5.  Two trains are running at 60 Kmph and 42 Kmph respectively, in same direction. Fast train completely passes a man sitting in the slower train in 30sec. What is the length of the faster train?

Answer: 150 m
Explanation:
Speed of the train = ( 60 - 42 ) Kmph ( ∴ Same direction Speed = first train - second train )
= 18 Kmph
Length = Speed * Time
Length = [ ( 18 * ( 5 / 18 ) ) * 30 ] m [ ∴ ( x ) kmph = ( x * ( 5 / 18 ) ) m/sec ]
= ( 5 * 30 ) m
= 150 m.


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

Answer: 55 kmph
Explanation:
Speed of the train relative to man = ( x + 5 ) kmph
= [ ( x + 5 ) * ( 5 / 18 ) ] m/sec
= [ ( 5x + 25 ) / 18 ] m/sec
⇒ 100 / [ ( x + 5 ) * ( 5 / 18 ) ] = 6
⇒ 100 * 18 / 5x + 25 = 6
1800 = 6 * ( 5x + 25 )
1800 = 30x + 150
3x = 1650
x = 1650 / 3
x = 55
Speed of the train 55 kmph.


7.  A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, Find the length of the train?

Answer: 120 m
Explanation:
Speed = [ 12 / ( 10 / 60 ) ] km/hr ( ∴ 1 hr = 60 min )
Speed = [ ( 12 * 60 ) / 10 ] km/hr
= 72 km/hr
= [ 72 * ( 5 / 18 ) ] m/sec
= ( 4 * 5 ) m/sec
= 20 m/sec
Length of the train = ( speed * time )
= ( 20 * 6 ) m
= 120 m.


8.  The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then find the speed of the first train?

Answer: 87.5 km/hr
Explanation:
Let the speed of two trains be 7x and 8x km/hr
8x = ( 400 / 4 )
8x = 100
x = 100 / 8
x = 12.5
Speed of first train = ( 7 * 12.5 ) km/hr
= 87.5 km/hr.


9.  A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?

Answer: 62 kmph
Explanation:
Relative speed = ( 280 / 9 ) m/sec
= ( 280 / 9 ) * ( 18 / 5 ) kmph
= 56 * 2
= 112 kmph
Speed of goods train = ( 112 - 50 ) kmph
= 62 kmph.


10.  320m long train is running at 72 Kmph. How much time it will take to cross a platform of 180m long?

Answer: 25 Sec
Explanation:
Total Length = Platform Length + Train Length
Total Length = 320 m + 180 m
= 500 m
Distance = Speed * Time
500 = 72 * Time
500 = 72 * ( 5 / 18 ) * Time
Time = 25 Sec.