# Trains, Boats and Streams

• Last Updated : 06 May, 2016

 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?
 2 km/h 1 km/h 6 km/h 4 km/h

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?
 25 km/h 21 km/h 26 km/h 22 km/h

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?
 5 h 4 h 6 h 3 h

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.
 24 h 21 h 23 h 22 h

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.
 10 km/h 15 km/h 12 km/h None of these

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?
 27 m/s 20 m/s 25 m/s 30 m/s

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?
 34 36 30 32

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?
 5 sec 4 sec 5.5 sec 4.5 sec

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?
 5 sec 4 sec 3 sec 3.5 sec

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?
 120 m 150 m 125 m 100 m

Question 10-Explanation:
relative distance = L+80 V = D/T 90  =( L+80)/2 = 100 meters
There are 15 questions to complete.