 # Time & Distance (3)

1. A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
1. None of these
2. 280 meter
3. 240 meter
4. 200 meter

Explanation :-

Speed of the train = 54 km/h = 54 *5/18 m/s = 15 m/s
Length of the train = speed*time = 15 * 20 = 300 m
Let the length of the platform be x metres
Therefore , [ (x + 300) / 36 ] = 15
x + 300 = 540
x =  240 m

2. A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
1. 79.2 km/hr
2. 69 km/hr
3. 74 km/hr
4. 61 km/hr

Explanation :-

Let the length of the train be x metres
& speed of the train be y m/sec
Therefore ,
x/8 = y    => x = 8y
&   (x + 264)/20 = y
From above equations
(8y + 264)/20 = y
8y + 264 = 20 y
y = 22 m/sec = (22 * 18/5) = 79.2 km/h

3. Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?
1. 10
2. 25
3. 12
4. 20

Explanation :-

Speed of train 1 = (120/10) = 12 m/sec
Speed of train 2 =  (120/15) = 8 m/sec
As they are moving in opposite direction
Therefore ,
Relative speed = 12 + 8 = 20 m/sec
Distance covered = 120 + 120 = 240 m
Time = distance/speed = 240/20 = 12 sec

4. Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
1. 2 : 3
2. 2 :1
3. 4 : 3
4. 3 : 2

Explanation :-

Speed = Distance / Time
Speed of First train = Distance/9
Speed of Second Train = Distance/16
Ratio of their Speeds = (Distance/9)  (Distance/16)
Ratio of their Speeds = (1/9) : (1/16) = (1/3) : (1/4) = 4 : 3

5. A train having a length of 1/4 mile , is traveling at a speed of 75 mph. It enters a tunnel 3 ½ miles long. How long does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
1. 3 min
2. 4.2 min
3. 3.4 min
4. 5.5 min