 # Time & Distance (16)

1. A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?
1. 1250
2. 1280
3. 1320
4. 1340

Explanation :-

Speed = 5 km/h = 5 *(5/18) m/s = 25/18 m/s
Time = 15 minute = 15*60 seconds = 900 sec
Distance = Speed * Time = (25/18) * 900 = 1250 m/s

2. A train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?
1. 6 hrs 21 min
2. 7 hrs 14 min
3. 7 hrs 22 min
4. 6 hrs

Explanation :-

Time taken to cover 600 km = 6 hours [because train speed is 100 km/hr] No. of Stops = (600/75) – 1  = 8 – 1 = 7 (Stoppage Time for Last stop exluded)
Time Spent on stops = 7*3 = 21 minutes
Total time to travel = 6 hrs + 21 minutes

3. If a train runs at 40 km/hour, it reaches its destination late by 11 minutes. But if it runs at 50 km/hour, it is late by 5 minutes only. The correct time (in minutes) for the train to complete the journey is?
1. 13
2. 15
3. 19
4. 21
5. None of these

Explanation :-

Let the distance be x km
Time taken with speed 40 km/h = x/40
Time taken with speed 50 km/h = x/50
Difference between these two time is (11-5) = 6 min.= 1/10 hour
(x/40) – (x/50) = 1/6
(5x – 4x)/200 = 1/6
x = 20,  Therefore
Time taken with speed 40 km/h = x/40 = 20/40 = 1/2 hours = 30 min
It is 11 min lat , So correct time = 30-11 = 19 min.

4. Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
1. 15 hours
2. 16 hours
3. 17 hours
4. 18 hours
5. None of these

Explanation :-
The relative speed of the boys = 5.5kmph – 5kmph  = 0.5 km/h
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 km/h = 17 hrs

5. 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?
1.11:9
2.13:9
3.17:9
4.21:9
5.None of these