 # Time & Distance (4)

1. A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
1. 270 m
2. 210 m
3. 340 m
4. 130 m

Explanation :-

Let the length of the train be x meters.
Speed of Train = 72 km/h =72*(5/18) m/sec = 20 m/sec
Time = 26 seconds
Speed = Distance /Time
20 = (x+250)/26
(x + 250) = 520
x = 270 meters
Length of the goods train = 270 meter

2. A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
1. 62 m
2. 54 m
3. 50 m
4. 55 m

Explanation :-

Lets suppose the length of train = x metre and speed = y m/sec
Speed of First person = 2 km/h = 2*(5/18) = 5/9 m/sec
Speed of Second person = 4 km/h = 4*(5/18) = 10/9 m/sec
Relative speed = Total distance / time
y – (5/9) = x/9    &    y – (10/9) = x/10  (Speeds are subtracted because of opposite Direction)
9y – 5 = x      &     10(9y – 10) = 9x
9y = x + 5     &      9y = (9x /10)+10
On solving, we get: x = 50.
Length of the train is 50 m.

3. A train is traveling at 48 kmph . It crosses another train having half of its length , traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. What is the length of the platform?
1. 500 m
2. 360 m
3. 480 m
4. 400 m

Explanation :-

Let the length of the First Train be x .metres
Therefore, Length of the Secondt train = x/2 metres
Relative speed = (48 + 42) km/h = 90*(5/18) m/sec = 25 m/sec
[x + (x/2)] /25 = 12       => 3x/2 = 300      => x = 200
Length of first train = 200 m.
Let the length of platform be y metres.
Speed of the First Train = 48 *(5/18) m/s = 40/3
40/3 = (200 + y) / 45
600 + 3y = 1800
y = 400 m

4. A train having a length of 270 meter is running at the speed of 120 kmph . It crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
1. 320 m
2. 190 m
3. 210 m
4. 230 m

Explanation :-

As trains are running in opposite direction, Therefore
Relative speed = 120 +80 = 200 km/h = 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter
(x + 270)/9 = 500/9
x + 270 = 500
x = 230

5. Two trains, each 100 m long are moving in opposite directions. They cross each other in 8 seconds. If one is moving twice as fast the other, the speed of the faster train is
1. 75 km/hr
2. 60 km/hr
3. 35 km/hr
4. 70 km/hr