# Time & Distance (8)

1. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
1. 26 minutes and 18 seconds
2. 42 minutes and 36 seconds
3. 45 minutes
4. 46 minutes and 12 seconds

Explanation :-

Time taken by A to complete the circle = 252 sec.
Time taken by B to complete the circle = 308 sec.
Time taken by C to complete the circle = 198 sec.
They will again at starting together after,
LCM of 252, 308 and 198.
252 = 2 *2 *3*3*7        308 = 2 *2*7*11         198 = 2 *3*3*11
LCM = 2*2*3*3*7*11 = 2772 seconds
=> 46 minutes 12 seconds.

2. The stream of a boat when travelling downstream is 32 km/hr, whereas when travelling upstream it is 28km/hr. what is the speed of boat in still water?
1. 27km/hr
2. 30km/hr
3. 31km/hr
4. Cannot be determined

Explanation :-

Speed of boat in still water =  (32+28)/2 = 60/2 = 30km/hr

3. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
1. 35.55 km/hr
2. 36 km/hr
3. 71.11 km/hr
4. 71 km/hr
5. 69.69km/hr

Explanation :-

Time = Distance/speed
Time taken to Complete first 160 km with speed 64 km/h = (160/64) = 10/4 hrs
Time taken to Complete last 160 km with speed 80 km/h = (160/80) = 2 hrs
Total Time = (10/4) + 2 = 9/2 hrs
Time taken for 320 Km = 320/(9/2) = 71.11km/hr

4. A train travelling at 36 kmph completely crosses another train having half its length and travelling in the opposite direction at 54 kmph, in 12 seconds. If it also passes a railway platform in 112 minutes, the length of the platform is :
1. 560 metres
2. 620 metres
3. 700 meres
4. 750 metres
5. 720 meters

Explanation :-

Let the length of slower train =x metres
Therefore , the length of faster train = (x/2) meters.
Relative speed = (36 + 54) km/hr = (90×5/18) m/sec = 25 m/sec
3x/(2×25) = 12
3x = 600
x = 200 m
Length of slower train = 200 m
Let the length of platform be y metres
Then, (200 + y)/(36 + 5/18) = 90
200 + y = 900
y = 700 m
Length of platform = 700 m

5. A man travels 35 km partly at 4 km/hr and at 5 km/hr. If he covers former distance at 5 km/hr and later distance at 4 km/hr, he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is
1. 9 hours
2. 7 hours
3. 9/2 hours
4. 8 hours
5. 10 hours