Quantitative Aptitude

Boats and Streams

369 Questions
All Recover still-water and stream speeds 136 Calculate one-way and round-trip time 61 Ratio of boat to stream speed 54 Use time differences and equal-distance ratios 39 Perpendicular river crossing 36 Round-trip average speed 14 Angles of drift 12 Handle drifting objects 8 Solve meeting and separation problems 6 Fixed-time distance ratios 3

Boats and Streams Questions

Multiple choice

There is a road besides a river. Two friends Ram and Shyam started from a place A, moved to a temple situated at another place B and then returned to A again. Ram moves on a cycle at a speed of 12 km/h, while Shyam sails on a boat at a speed of 10 km/h. If the river flows at the speed of 4 km/h, which of the two friends will return to place A first?

  1. Ram

  2. Shyam

  3. Both will return simultaneously

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A professional boat rower can row a distance of 15 miles in still water in 1 hour. In a competition, he has to row to a certain point and back in running water, going in his preferred direction first. He covers a distance of 260 miles and back in 1 day and 16 hours. What could be the speed of water in the stream?

  1. 4.40 miles/h

  2. 5.48 miles/h

  3. 6.15 miles/h

  4. 7.47 miles/h

  5. 8.28 miles/h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the speed of the boat (15 mph) and s be the speed of the stream. Total time = 40 hours. Distance = 260 miles. 260/(15+s) + 260/(15-s) = 40. Simplifying: 260(15-s + 15+s) / (225-s^2) = 40; 260(30) / (225-s^2) = 40; 7800 / (225-s^2) = 40; 195 = 225 - s^2; s^2 = 30; s = sqrt(30) approx 5.477.

Multiple choice

A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is

  1. 3(3 - 5 )

  2. 12( 5 - 2)

  3. 3(3 + 5 )

  4. 3( 5 - 1)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be boat speed and c be current. Downstream: v+c = distance/2. Upstream: v-c = distance/3. Let distance = 6. v+c = 3, v-c = 2. 2v = 5, v = 2.5, c = 0.5. Second boat: total time 6 hours. Let speed be u. (6/(u+0.5)) + (6/(u-0.5)) = 6. 1/(u+0.5) + 1/(u-0.5) = 1. (u-0.5 + u+0.5) / (u^2 - 0.25) = 1. 2u = u^2 - 0.25. u^2 - 2u - 0.25 = 0. u = (2 + sqrt(4 - 4(1)(-0.25))) / 2 = (2 + sqrt(5)) / 2 = 1 + sqrt(5)/2. Time = 6 / (1 + sqrt(5)/2 + 0.5) = 6 / (1.5 + sqrt(5)/2) = 12 / (3 + sqrt(5)). Rationalizing: 12(3-sqrt(5)) / (9-5) = 3(3-sqrt(5)).

Multiple choice

A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day boat starts from point A, goes downstream for 1 hour, then upstream for 1 hour and repeats this four more times, that is, 5 upstream and 5 downstream journeys. Then the boat will be

  1. 20 km downstream of A

  2. 15 km downstream of A

  3. 22.5 km downstream of A

  4. 12.5 km downstream of A
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Upstream speed = 96/8 = 12 km/hr. Downstream speed = 96/6 = 16 km/hr. Let boat speed be B and stream speed be S. B-S=12, B+S=16. Adding gives 2B=28, B=14. Subtracting gives 2S=4, S=2. In 1 hour downstream, it goes 16 km. In 1 hour upstream, it goes 12 km. Net displacement per 2-hour cycle = 16 - 12 = 4 km downstream. In 5 cycles (10 hours), total displacement = 5 * 4 = 20 km downstream.

Multiple choice

A boat owner, eager to test the capabilities of his boat, sets off on a river journey. The boat travels 120 km upstream in 10 hours and covers the same distance downstream in 8 hours. On the following day, the boat departs from a point X and follows a pattern: it travels downstream for 2 hours, followed by upstream for 2 hours. This cycle is repeated for a total of 4 times. After completing these 4 cycles, what will be the boat's position relative to its starting point X?

  1. 16 km downstream of point X

  2. 24 km downstream of point X

  3. 28 km downstream of point X

  4. 38 km downstream of point X
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upstream speed = 120/10 = 12 km/h. Downstream speed = 120/8 = 15 km/h. Boat speed = (15+12)/2 = 13.5 km/h, stream speed = (15-12)/2 = 1.5 km/h. In one cycle (2h down, 2h up): distance = (15*2) - (12*2) = 6 km downstream. Total for 4 cycles = 6 * 4 = 24 km.

Multiple choice

A man goes from city A to city B situated 60 kms apart by a boat. His onward journey was with the stream while the return journey was an upstream journey. It took him four and half hours to complete the round trip. If the speed of the stream is 10 km/hr. How long did it take him to complete the onward journey?

  1. 3 hours

  2. 3.5 hours

  3. 2.25 hours

  4. 1.5 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let b be boat speed, s=10. Downstream speed = b+10, Upstream = b-10. 60/(b+10) + 60/(b-10) = 4.5. 60(b-10+b+10) / (b^2-100) = 4.5. 120b / (b^2-100) = 4.5. 120b = 4.5b^2 - 450. 4.5b^2 - 120b - 450 = 0. Divide by 1.5: 3b^2 - 80b - 300 = 0. (3b+10)(b-30) = 0. b = 30. Onward journey (downstream) = 60 / (30+10) = 60/40 = 1.5 hours.