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 person noticed that when the water is still, his boat can go at a speed of 16 km/hr. It takes 200% more time to go against the flow the water than going along with the flow for same distance. Find the difference between the speeds of water and boat in still water.

  1. 4 km/hr

  2. 5 km/hr

  3. 6 km/hr

  4. 8 km/hr

  5. 10 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let boat speed = 16, water speed = w. Downstream = 16+w, Upstream = 16-w. Time = Distance/Speed. 200% more time means 3 times the time. 1/(16-w) = 3 * 1/(16+w). 16+w = 48-3w. 4w = 32. w = 8. Difference = 16 - 8 = 8.

Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities. Quantity I: A boat travels 6 km upstream and returns back to the starting point in 2 hours. The speed of the boat in still water, if the speed of water is 4 kmph, is: Quantity II: A boat travels 15 km upstream ans returns back to the starting point in 4 hours. The speed of the boat in still water, if the speed of water is 5 kmph, is:

  1. Quantity I ≥ Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I > Quantity II

  5. Quantity I = Quantity II, or No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Swati can row a boat in still water at a speed of 5 km/hr. However, in a given river, it takes her 1 hour more to row the boat 12 km upstream than downstream. One day, Swati rows the boat in this river from X to Y, which is N km upstream from X. Then she rows back to X immediately. If she takes at least 2 hours to complete this round trip, what is the minimum possible value of N?

  1. 2

  2. 2.1

  3. 4.8

  4. 3.6

  5. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed of stream be v. Upstream speed = 5-v, downstream = 5+v. Time difference: 12/(5-v) - 12/(5+v) = 1. Solving gives v=1. Round trip time for distance N: N/(5-v) + N/(5+v) = N/4 + N/6 = 5N/12. We need 5N/12 >= 2, so N >= 24/5 = 4.8.

Multiple choice

A boat crosses a river with a velocity of 8 km/h. If the resulting velocity of boat is 10 km/h then the velocity of river water is

  1. 4 km/h

  2. 6 km/h

  3. 8 km/h

  4. 10 km/h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The resulting velocity is the vector sum of the boat velocity and river velocity. Assuming the boat crosses perpendicular to the flow, the resulting velocity squared is (boat velocity)^2 + (river velocity)^2. 10^2 = 8^2 + v_r^2, so 100 = 64 + v_r^2, v_r^2 = 36, v_r = 6 km/h.

Multiple choice

Speeds of Boat A and B in still water are in the ratio of 3:2 Rate of current is 10 Km/hr. Both Boats started from Point P to point Q downstream at the same time. After Boat B reaching Point Q, in return journey, it is powered by engine due to which the speed of the boat in still water is increased by 70%, while retuned Boat A returned to Point Q as usual. Both the boats returned back to point P at the same time. Then what is the speed of Boat A?

  1. 20 Km/hr

  2. 30 Km/hr

  3. 40 Km/hr

  4. 50 Km/hr

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Boat A's still-water speed be 3x and Boat B's be 2x. Equating their total travel times, including Boat B's increased return speed, gives x = 10, so Boat A's speed is 3x = 30 km/hr.

Multiple choice

Two boats go downstream from point X to point Y. The faster boat covers the distance from X to Y 1.5 times as fast as the slower boat. It is known that for every hour the slower boat lags behind the faster boat by 8 km. However if they go upstream then the faster boat covers the distance from Y to X in half the time as the slower boat. Find the speed of the slower boat in still water?

  1. 8 km/h

  2. 10 km/h

  3. 14 km/h

  4. 12 km/h

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

Brad and Angelina are on a boat. If they travel along the stream, they can travel at the speed of 22 km per hour; but if they travel upstream, they can travel at the speed of 10 km per hour. Find out the ratio of the speed of boat in still water to the speed of stream.

  1. 8 : 3

  2. 14 : 5

  3. 29 : 17

  4. 20 : 9

  5. 10 : 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement 1: x - 6 = 0.5x implies x = 12. Sufficient. Statement 2: x + 3 = 3(x - 7) implies x + 3 = 3x - 21, so 2x = 24, x = 12. Sufficient. Both are independently sufficient.

Multiple choice

The ratio of the speed of a boat in the still water and the speed of the stream is 7 : 5. The ratio of the speed of the stream to the speed of another boat in still water is 6 : 8. What is the ratio of the speed of the first boat to that of the second boat in still water?

  1. 19 : 20

  2. 20 : 21

  3. 21 : 20

  4. 23 : 21

  5. 25 : 23
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v1, v2 be boat speeds and s be stream speed. v1/s = 7/5. s/v2 = 6/8 = 3/4. We want v1/v2. v1 = (7/5)s. v2 = (4/3)s. v1/v2 = (7/5) / (4/3) = 21/20.