Trains, Boats and Streams


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Question 1
A boatman takes 3 hours 45 minutes to travel 15 km downstream and takes 2 hours 30 minutes to travel 5 km upstream of a river. What is the speed of the stream of the river in km/h?
A
2 km/h
B
1 km/h
C
6 km/h
D
4 km/h
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Question 1 Explanation: 
Downstream: Time taken = 3 + 45/60 = 3 + 3/4 = 15/4 h. Distance covered = 15 km. Downstream Speed = 15 / (15/4) = 4 km/h. Upstream: Time taken = 2 + 30/60 = 2 + 1/2 = 5/2 h. Distance covered = 5 km. Upstream Speed = 5 / (5/2) = 2 km/h. We know, speed of stream = 1/2 (Downstream Speed - Upstream Speed) = 1/2 (4-2) = 1 km/h.
Question 2
A speedboat runs 6 km upstream in a river and comes back to the starting point in 33 minutes. The stream of the river is running at 2 km/hr. What is the speed of speedboat in still water?
A
25 km/h
B
21 km/h
C
26 km/h
D
22 km/h
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Question 2 Explanation: 
Let the speed of speedboat in still water be x km/h. Then, speed downstream = (x + 2) km/h, speed upstream = (x - 2) km/h. Since it goes 6 km upstream and comes back in 33 minutes, we have 6/(x+2) + 6/(x-2) = 33/60 ⇒ 11x² - 240x - 44 = 0 ⇒ 11x² - 242x + 2x - 44 = 0 ⇒ (x - 22)(11x + 2) = 0 ⇒ x = 22. Therefore, the required speed = 22 km/h.
Question 3
A boat runs at the speed of 13 km/h in still water. If the speed of the stream is 4 km/h, how much time will it take to go 68 km downstream?
A
5 h
B
4 h
C
6 h
D
3 h
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Question 3 Explanation: 
Speed of the boat downstream = 13 + 4 = 17 km/h. Therefore, time taken to go 68 km downstream = (68/17) = 4 h.
Question 4
Peter's speedboat run at a speed of 9 km/h in still water. He rows to a place at a distance of 105 km and comes back to the starting point. If the speed of stream is 1.5 km/h, find out the time taken by Peter.
A
24 h
B
21 h
C
23 h
D
22 h
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Question 4 Explanation: 
Upstream speed = 9 - 1.5 = 7.5 km/h. Downstream speed = 9 + 1.5 = 10.5 km/h. Therefore, time taken = 105/7.5 + 105/10.5 = 14 + 10 = 24 h.
Question 5
A motorboat crosses a certain distance in 1 hour and comes back in 1½ hours. If the stream is running at 3 km/h, find out the speed of motorboat in still water.
A
10 km/h
B
15 km/h
C
12 km/h
D
None of these
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Question 5 Explanation: 
Let the speed of motorboat in still water be x km/h. Then, Downstream speed = (x + 3) km/h. Upstream speed = (x - 3) km/h. Then, (x + 3) × 1 = (x - 3) × 3/2 ⇒ 2x + 6 = 3x - 9 ⇒ x = 15. So, the speed of motorboat in still water is 15 km/h.
Question 6
A train crosses a pole in 20 sec. If the length of train is 500 meters, what is the speed of the train?
A
27 m/s
B
20 m/s
C
25 m/s
D
30 m/s
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Question 6 Explanation: 
V = 500/20 = 25 m/sV = 500/20 = 25 m/s
Question 7
A train crosses a pole in 10 sec. If the length of train is 100 meters, what is the speed of the train in Kmph?
A
34
B
36
C
30
D
32
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Question 7 Explanation: 
V = 100/10 = 10 m/s = 10*3600/1000 = 36Km/hr
Question 8
A train is running at a speed of 100Kmph. A car is running on road parallel to the train’s track at a speed of 20 Kmph in the same direction as of train. How much time will it take to cross the car if the length of the train is 100 meters?
A
5 sec
B
4 sec
C
5.5 sec
D
4.5 sec
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Question 8 Explanation: 
Relative speed of train = 100-20 Kmph (say car is stopped) T = D/V = 0.100/80 = .00125 hrs => 00125*3600 = 4.5 secs
Question 9
A train is running at a speed of 100Kmph. A car is running on road parallel to the train’s track at a speed of 20 Kmph opposite to train. How much time will it take to cross the car if the length of the train is 100 meters?
A
5 sec
B
4 sec
C
3 sec
D
3.5 sec
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Question 9 Explanation: 
Relative speed of train = 100+20 Kmph (say car is stopped) T = D/V = 0.100/120 = .000833 hrs => 000833*3600 = 3 secs
Question 10
What is the length of the platform, if a train running at a speed of 90 m/sec and length is 80 meters, crosses the platform in 2 sec?
A
120 m
B
150 m
C
125 m
D
100 m
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Question 10 Explanation: 
relative distance = L+80 V = D/T 90  =( L+80)/2 = 100 meters
There are 15 questions to complete.
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