 # Time & Distance (5)

1. Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
1. 10.30 a.m
2. 10 a.m.
3. 9.10 a.m.
4. 11 a.m.

Explanation :-

Lets suppose both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = (20x) km
Distance covered by train starting from Q in (x-1) hours = 25(x-1) km
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x = 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

2. A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
1. 81 km/hr
2. 88 km/hr
3. 62 km/hr
4. 46 km/hr

Explanation :-

Speed of 1st person = 4 km/h = 4.5 x (5/18)  m/s = 5/4 m/s = 1.25 m/s
Speed of 2nd person = 5.4 km/h = 5.4 x (5/18) m/s = 3/2 m/s = 1.5 m/s
Let speed of train be x m/s.
Therefore ,
(x – 1.25) * 8.4 = (x – 1.5) * 8.5
0.1x = 2.25
x = 22.5
Speed of the train = 22.5 * 18/5 = 81 km/h

3. A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
1. 10 sec
2. 8 sec
3. 6 sec
4. 4 sec

Explanation :-
Distance = 110 m
Relative speed = 60 + 6 = 66 km/h = 66* 5/18 m/sec = 55/3 m/sec
Time taken to pass the man = 110/(55/3) = 100*3/55 = 6 s

4. A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?
1. 150 m
2. 350 m
3. 420 m
4. 600 m

Explanation :-

Speed = Distance/time = 300/18 = 50/3 m/sec
Let the length of the platform be x meters
While crossing plateform , total distance = x + 300  Time = 39 sec
x + 300 = (50/3)*39
x + 300 = 650
x = 350 m

5. A train crosses a post in 15 seconds and a platform 100 m long in 25 seconds. Its length is
1. 150 m
2. 300 m
3. 400 m
4. 180 m