Boats and Streams Aptitude

Boats and Streams problems are a crucial part of aptitude tests, involving calculations based on the movement of boats in still water and the effect of the stream’s current. The key concepts include the speed of the boat in still water, the speed of the stream (current), and the effective speed of the boat downstream (with the current) and upstream (against the current).

1. If the speed of a boat in still water is 10 km/hr and the speed of the stream is 2 km/hr, what is the boat's speed downstream?

Downstream speed = Speed of boat + Speed of stream = 10 + 2 = 12 km/hr.

2. A boat goes 6 km upstream and 10 km downstream in 4 hours. If the speed of the stream is 1 km/hr, what is the speed of the boat in still water?

Let the speed of the boat in still water be x km/hr.
Upstream speed = x - 1, downstream speed = x + 1.
Time upstream = 6 / (x - 1), time downstream = 10 / (x + 1).
Total time = 6 / (x - 1) + 10 / (x + 1) = 4.
Solve for x to get x = 5 km/hr.

3. The speed of a boat in still water is 15 km/hr, and the rate of the stream is 3 km/hr. How long will it take to go 60 km downstream?

Downstream speed = 15 + 3 = 18 km/hr.
Time = Distance / Speed = 60 / 18 = 3.33 hours ≈ 3 hours.

4. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in still water?

Speed upstream = 2 km/hr, speed downstream = 6 km/hr.
Speed in still water = 1/2(Upstream speed + Downstream speed) = 1/2(2 + 6) = 4 km/hr.
Time to go 5 km = 5 / 4 = 1.25 hours ≈ 1.25 hours.

5. If a boat goes 30 km upstream in 6 hours and 44 km downstream in 4 hours, what is the speed of the boat in still water?

Speed upstream = 30/6 = 5 km/hr, speed downstream = 44/4 = 11 km/hr.
Speed in still water = 1/2(Upstream speed + Downstream speed) = 1/2(5 + 11) = 8 km/hr.

6. The speed of a boat in still water is 20 km/hr, and the speed of the stream is 4 km/hr. The boat takes 2 hours more in upstream than in the downstream to cover the same distance. What is the distance?

Let the distance be x km.
Upstream speed = 20 - 4 = 16 km/hr, downstream speed = 20 + 4 = 24 km/hr.
Time upstream - time downstream = x/16 - x/24 = 2.
Solve for x to get x = 24 km.

7. A man rows 18 km downstream in 3 hours and returns upstream in 6 hours. The speed of the stream is:

Speed downstream = 18/3 = 6 km/hr, speed upstream = 18/6 = 3 km/hr.
Speed of the stream = 1/2(Downstream speed - Upstream speed) = 1/2(6 - 3) = 1.5 km/hr.

8. If the speed of a boat in still water is 7 km/hr and the speed of the stream is 3 km/hr, the boat takes 10 hours to go to a place and come back. The distance of the place is:

Let the distance be x km.
Time upstream = x/(7 - 3), time downstream = x/(7 + 3).
x/(7 - 3) + x/(7 + 3) = 10.
Solve for x to get x = 30 km.

9. A boat covers a certain distance downstream in 1 hour, while it comes back in 1.5 hours. If the speed of the stream is 2 km/hr, what is the speed of the boat in still water?

Let the speed of the boat be x km/hr.
Speed downstream = x + 2, speed upstream = x - 2.
Distance = (x + 2) * 1 = (x - 2) * 1.5.
Solve for x to get x = 8 km/hr.

10. The speed of a boat in still water is 15 km/hr, and the speed of the stream is 5 km/hr. The distance traveled downstream in 2.5 hours is:

Speed downstream = 15 + 5 = 20 km/hr.
Distance = Speed * Time = 20 * 2.5 = 50 km.

11. A man rows to a place at a distance of 45 km and comes back to the starting point. The total time taken by him is 12 hours. If the speed of the stream is 3 km/hr, find the speed of the boat in still water.

Let the speed of the boat be x km/hr.
Time upstream = 45/(x - 3), time downstream = 45/(x + 3).
45/(x - 3) + 45/(x + 3) = 12.
Solve for x to get x = 9 km/hr.

12. A boat takes 4 hours to travel a distance downstream and returns upstream in 6 hours. If the speed of the stream is 2 km/hr, find the distance covered.

Let the speed of the boat be x km/hr.
Speed downstream = x + 2, speed upstream = x - 2.
Distance downstream = (x + 2) * 4, distance upstream = (x - 2) * 6.
Since both distances are equal, solve for x to get x and then the distance.

13. A boatman rows to a place 45 km away and back in 20 hours. If the speed of the boat in still water is 5 km/hr, find the speed of the stream.

Let the speed of the stream be y km/hr.
Time upstream = 45/(5 - y), time downstream = 45/(5 + y).
45/(5 - y) + 45/(5 + y) = 20.
Solve for y to get y = 1.5 km/hr.

14. A man can row at 10 km/hr in still water. If the river is running at 3 km/hr, it takes him 4 hours longer to row up than to row down the river. Find the distance.

Let the distance be x km.
Speed downstream = 10 + 3 = 13 km/hr, speed upstream = 10 - 3 = 7 km/hr.
Time downstream = x / 13, time upstream = x / 7.
Time upstream - time downstream = 4 hours.
x/7 - x/13 = 4.
Solve for x to get x = 72 km.

15. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream?

Let the speed of the stream be x km/hr.
Speed downstream = 15 + x, speed upstream = 15 - x.
Time downstream = 30 / (15 + x), time upstream = 30 / (15 - x).
Total time = 4.5 hours.
30/(15 + x) + 30/(15 - x) = 4.5.
Solve for x to get x = 5 km/hr.

16. If a boat takes 8 hours to row a distance upstream and 3 hours to row the same distance downstream, what is the ratio of the speed of the boat in still water to the speed of the stream?

Let the speed of the boat be b km/hr and the speed of the stream be s km/hr.
Upstream speed = b - s, downstream speed = b + s.
b - s = Distance / 8, b + s = Distance / 3.
Divide the two equations to get the ratio b:s = 4:3.

17. A man rows upstream at 8 km/hr and downstream at 13 km/hr. The speed of the stream is:

Speed of the stream = 1/2(Downstream speed - Upstream speed) = 1/2(13 - 8) = 2.5 km/hr.

18. A boat goes 20 km upstream in 4 hours and 36 km downstream in 6 hours. The speed of the boat in still water is:

Upstream speed = 20/4 = 5 km/hr, downstream speed = 36/6 = 6 km/hr.
Speed in still water = 1/2(Upstream speed + Downstream speed) = 1/2(5 + 6) = 5.5 km/hr.

19. A boatman can row to a place 48 km away and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The speed of the boat in still water is:

Let the speed of the boat be x km/hr and the speed of the stream be y km/hr.
4/(x + y) = 3/(x - y).
Solve for x and y using the equation and the total time for the trip.

20. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 km/hr, find the speed of the boat in still water.

Speed upstream = 7 / (42/60) km/hr = 10 km/hr.
Speed of the boat in still water = Speed upstream + Speed of stream = 10 + 3 = 13 km/hr.