Trains, Boats and Streams

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

Answer: (B)

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

Answer: (D)

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

Answer: (B)

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

Answer: (A)

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

Answer: (B)

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

Answer: (C)

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

Answer: (B)

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

Answer: (D)

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

Answer: (C)

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

Answer: (D)

relative distance = L+80 V = D/T 90  =( L+80)/2 = 100 meters