1. Train takes 4 seconds to pass a man. Another train travelling in opp. direction of same length takes 5 seconds to pass the man. Find the time taken by both trains to cross each other ?
A. 51/9 sec
B. 40/9 sec
C. 42/9 sec
D. 41/9 sec
E. None of these
Sol. Length of trains = x meter
Speed of 1st train = x/4 m/sec
Speed of 2nd train = x/5 m/sec
Relative speed = x/4 + x/5 = 9x/20 m/sec
Required Time = 2x/(9x/20) = 40/9 seconds.
2. A motor boat travelling at the same speed can cover 25 km upstream and 39 km downstream in 8 hrs. At the same speed, it can cover 35 km upstream and 52 km downstream in 11 hrs. Find the speed of the stream ?
A. 5
B. 6
C. 4
D. 3
E. None of these
Sol. Lets assume upstream speed to be 'x' km/hr
And downstream speed to be 'y' km/hr
Then, 25/x + 39/y = 8
And, 35/x + 52/y = 11
Solving these two,we get,
x = 5km/hr
y = 13 km/hr
Thus, speed of stream = (y - x)/2 = (13 - 5)/2 = 4 km/hr.
3. In a race of 100 meter , Rajiv beats Ajay by 40 meters , and Ajay beats Dhawan by 40 meters .If Rajiv completes the race in 9 seconds after how much time does Dhawan complete the race ?
A. 15 sec
B. 14 sec
C. 25 sec
D. 20 sec
E. None of these
Sol. When Rajiv runs 100m Ajay runs 60 m
Ratio of speeds = 5 : 3
Ratio of speeds of Ajay and Dhawan = 5 : 3
Ratio of their three Speeds = 25 : 15 : 9
Time is inverse to speed , So
1/25 : 1/15 : 1/9
9 : 15 : 25
Dhawan finishes in 25 seconds.
4. There are two trains of lengths 300 m and 200 m respectively. Both start at same time. If they travel in same direction they cross each other in 20 hours and if they travel in opposite direction towards each other, they cross each other in 2 hours. What is the speed of the fastest train ?
A. 135
B. 137
C. 137.5
D. 140
E. None of these
Sol. Let speed of 1st train = x km/hr, of 2nd train = y km/hr
Then when they travel in same direction, relative speed = x-y
So (300+200) = (x-y)*20. This gives x – y = 25
When they travel in opposite direction, relative speed = x+y
So (300+200) = (x+y)*2. This gives x + y = 250
Solve both equations, x = 137.5
5. If a car travels a distance of 300 km in 8 hours, partly at a speed of 40 kmh-1 and partly at 30 kmh-1, what is the distance it travelled at the speed of 40 kmh-1?
A. 200 km
B. 210 km
C. 220 km
D. 240 km
E. None of these
Sol. Lets assume at 40 km/hr the car covers 'x' km
Then at 30 km/hr it will cover '300-x' km
According tot he question, x/40 + (300-x)/30 = 8
Solving we get, x = 240 km.
6. A van covers a distance of 392 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 11 kmph more than that of the speed of the van to cover a distance which is 28 km more than that travelled by the van ?
A. 6
B. 5
C. 4
D. 7
E. None of these
Sol. Speed of the truck = Distance/time = 392/8 = 49 kmph
Now, speed of car = (speed of van + 11) kmph = (49 + 11) = 60 kmph
Distance travelled by car = 392 + 28 = 420 km
Time taken by car = Distance/Speed = 420/60 = 7 hours.
7. A person runs 1/2th of distance at 10 km/hr, the next 2/5th of distance at 8 km/hr and the rest of the distance at 6 km/hr. Find his average speed ?
A. 9
B. 8.67
C. 8.57
D. 8
E. None of these
Sol. Lets assume total distance to be 100 km.
Required Average = 100/[50/10 + 40/8 + 10/6] = 8.57 km/hr
8. 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?
A. 26 minutes and 18 seconds
B. 42 minutes and 36 seconds
C. 45 minutes
D. 46 minutes and 12 seconds
E. None of these
Sol. L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec.
i.e., 46 min. 12 sec.
9. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
A. 10
B. 15
C. 12
D. 20
E. None of these
Sol. Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train =120/15= 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore, required time =(120 + 120)/20 = 12 sec.
10. Two trains travel in opposite direction from the same starting point. Speeds of the 1st train is 22m/s and speed of 2nd train is 8m/s. How long will tey take to be 378 km apart ?
A. 3hours 30min
B. 3hours 45min
C. 4hours 15min
D. 3hours 35min
E. None of these.
Sol. Relative speed = 22 + 8 = 30m/s = 30*18/5 = 108 km/hr
Relative distance = 378 km
Thus time taken will be = 378/108 = 3hours 30minutes.
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