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

A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6.5 hours. Find the speed of the boat in still water and the speed of the stream (both in kmph).

  1. 9, 5

  2. 10, 4

  3. 12, 6

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let u be upstream speed and d be downstream speed. 24/u + 28/d = 6 and 30/u + 21/d = 6.5. Solving this system, we find u = 6 and d = 14. Speed of boat = (d+u)/2 = 10, speed of stream = (d-u)/2 = 4.

Multiple choice

On a river, B is an intermediate station equidistant from the stations A and C. A boat can go from A to B and come back in 6 hr. If it takes 4 hr to go from A to C, how long would it take to go from C to A?

  1. 4 hr

  2. 2 hr

  3. 8 hr

  4. 10 hr

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance AB = BC = d. Time A to B and back = 6h. Time A to C = 4h. A to C is 2d. If the boat takes 4h for 2d, it takes 2h for d. If it takes 6h to go A to B and back, and it takes 2h to go A to B, it must take 4h to go B to A. This implies the stream is helping one way and hindering the other. Calculating the speeds shows the return trip C to A takes 8 hours.

Multiple choice

The crew of a boat can row at the rate of 5 mph in still water. To row 24 miles against the stream, they take 4 times as long as to row the same distance down the river. Find the speed at which the river flows.

  1. 2 mph

  2. 2.5 mph

  3. 3 mph

  4. 3.5 mph

  5. 4 mph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be the speed of the stream. Speed downstream = 5 + v, speed upstream = 5 - v. Time = Distance / Speed. 24 / (5 - v) = 4 * (24 / (5 + v)). Simplifying gives 5 + v = 4(5 - v), so 5 + v = 20 - 4v, 5v = 15, v = 3 mph.

Multiple choice

The ratio of the speed of a boat in downstream direction to the speed of the stream is 12 : 1. If the speed of the stream is 3 km/hr, find the distance travelled upstream (in km) in 5 hours.

  1. 130

  2. 155

  3. 150

  4. 210

  5. 180
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed of boat in still water be u and stream be v. Downstream speed = u + v. Given (u+v)/v = 12/1, so u+v = 12v. Given v = 3, so u+v = 36 km/hr. Upstream speed = u - v = (12v - v) - v = 10v = 30 km/hr. Distance = speed * time = 30 * 5 = 150 km.

Multiple choice

The ratio of the speed of a motorboat to that of the water current is 32 : 8. The boat goes somewhere along the current for 4 hours and 45 minutes. How much time will it take to come back from there?

  1. 7 hours and 12 minutes

  2. 6 hours and 18 minutes

  3. 7 hours and 5 minutes

  4. 7 hours and 55 minutes

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed ratio boat:current = 32:8 = 4:1. Downstream speed = 4+1 = 5 units. Upstream speed = 4-1 = 3 units. Time taken downstream = 4.75 hours. Distance = 5 * 4.75 = 23.75 units. Time taken upstream = 23.75 / 3 = 7.9166 hours. 0.9166 * 60 = 55 minutes. Total = 7 hours 55 minutes.

Multiple choice

A boat travels 28 km upstream in 7 hours and 22.5 km downstream in 4 hours 30 minutes. Then, the speed of the boat in still water and the speed of the current, respectively is

  1. 4.5 km/h and 0.5 km/h

  2. 6.5 km/h and 0.6 km/h

  3. 5.5 km/h and 5 km/h

  4. 9 km/h and 0.9 km/h

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

Upstream speed = 28/7 = 4 km/h. Downstream speed = 22.5 / 4.5 = 5 km/h. Boat speed = (5+4)/2 = 4.5 km/h. Current speed = (5-4)/2 = 0.5 km/h.

Multiple choice

Albert can row a boat 32 km upstream and 45 km downstream in 17 hours. Also, he can row 40 km upstream and 55 km downstream in 21 hours. The speeds of the stream and the boat in still water, respectively, are

  1. 2 km/hr and 8 km/hr

  2. 1.75 km/hr and 7.25 km/hr

  3. 0.5 km/hr and 4.5 km/hr

  4. 0.5 km/hr and 4 km/hr

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u = upstream speed, d = downstream speed. 32/u + 45/d = 17 and 40/u + 55/d = 21. Solving this system: let x=1/u, y=1/d. 32x+45y=17, 40x+55y=21. Multiplying by 5 and 4: 160x+225y=85, 160x+220y=84. So 5y=1, y=0.2, d=5. Then 32x + 9 = 17, 32x=8, x=0.25, u=4. Boat speed = (d+u)/2 = 4.5, stream = (d-u)/2 = 0.5.

Multiple choice

A man rows 54 km downstream in 6 hours and 35 km upstream in 7 hours. Find the time taken by the man to row 48 km upstream, if speed of the boat in still water is increased by 14.28%.

  1. 6 hours

  2. 4 hours

  3. 8 hours

  4. 11 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 54/6 = 9 km/hr. Upstream speed = 35/7 = 5 km/hr. Boat speed = (9+5)/2 = 7 km/hr. Stream speed = (9-5)/2 = 2 km/hr. New boat speed = 7 * 1.1428 = 8 km/hr. New upstream speed = 8 - 2 = 6 km/hr. Time for 48 km = 48/6 = 8 hours.