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 $12km$ upstream and $40km$ downstream in $8$hrs. It can go $16km$ downstream in the same time. Find the speed of the boat in still water and the speed of the stream.
  1. Speed of boat in still water $=9km/hr$ and speed of stream $6km/hr$.
  2. Speed of boat in still water $=6km/hr$ and speed of stream $2km/hr$.
  3. Speed of boat in still water $=14km/hr$ and speed of stream $32km/hr$.
  4. Speed of boat in still water $=7km/hr$ and speed of stream $23km/hr$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. If x represents the speed of the boat in still water in km/hr and y represents the speed of the stream in km/hr, then _________.
  1. $x + y = 11, x-y= 5$
  2. $x + y = 5, x - y = 11$
  3. $x + y = 6, x - y = 10$
  4. $x + y = 10, x - y = 6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let u = 1/(x-y) and v = 1/(x+y). 30u + 44v = 10 and 40u + 55v = 13. Solving the system: 120u + 176v = 40 and 120u + 165v = 39. Subtracting gives 11v = 1, so v = 1/11. Thus x+y = 11. Substituting v into the first eq: 30u + 4 = 10, 30u = 6, u = 1/5. Thus x-y = 5.

Multiple choice

The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boating till water.
  1. Speed of boat = 8 km/h & Speed of stream $= 3$ km/hr
  2. Speed of boat = 8 km/h & Speed of stream $= 4$ km/hr
  3. Speed of boat = 7 km/h & Speed of stream $= 2$ km/hr

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 30/u + 44/v = 10 and 40/u + 55/v = 13. Solving this system yields u = 5 km/h and v = 11 km/h. Boat speed = (11+5)/2 = 8 km/h; stream speed = (11-5)/2 = 3 km/h.

Multiple choice

The ratio of speeds of a motor boat to that of the current of water is $36:5$. The motor boat goes along with the current is $5$ hr $10$ min. Find the time to come back of motor boat ?
  1. $6$ hr, $50$ min
  2. $5$ hr, $40$ min
  3. $7$ hrs
  4. $6$ hr, $30$ min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speed of boat be 36k and current be 5k. Downstream speed is 41k, upstream is 31k. Distance = 41k * (310/60) hours. Time taken upstream = Distance / 31k = (41k * 310/60) / 31k = 41 * 310 / (60 * 31) = 41 * 310 / 1860 = 12710 / 1860 = 6.833 hours, which is 6 hours and 50 minutes.

Multiple choice

It takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstream. If the speed of the boat is x mph and the speed of the current is y mph, then what is the speed of the boat in still water and how fast is the current?

  1. 3 mph, 9 mph

  2. 9 mph, 3 mph

  3. 7 mph, 2 mph

  4. 8 mph, 5 mph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Downstream speed (x + y) = 24/2 = 12 mph. Upstream speed (x - y) = 18/3 = 6 mph. Solving the system: 2x = 18 implies x = 9, and 9 + y = 12 implies y = 3.

Multiple choice

A boat travelled 336 miles upstream and downstream. If the boat takes 14 hours to travel upstream and 12 hours to travel downstream, find the speed of boat in still water and speed of the current.

  1. Boat = 28 mph; Current = 4mph

  2. Boat = 26 mph; Current = 2 mph

  3. Boat = 26 mph; Current = 4 mph

  4. Boat = 28 mph; Current = 2 mph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upstream speed = 336 / 14 = 24 mph. Downstream speed = 336 / 12 = 28 mph. Boat speed = (28 + 24) / 2 = 26 mph. Current speed = (28 - 24) / 2 = 2 mph.

Multiple choice

Directions: Compare the two quantities in A and B. A boat traveled upstream a distance of 90 miles at an average speed of (V - 3) miles per hour and then traveled the same distance downstream at an average of (V + 3) miles per hour. If the trip upstream took half an hour longer than the trip downstream. x = Hours did it take the boat to travel downstreamy = Hours did it take the boat to travel upstream Quantity A Quantity B 6x 5y

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

The speed of a boat in still water is 9 km/h and the speed of the stream is 3 km/h. The boat rows to a place which is 47 km away and returns from the same path. Find the average speed of the boat during the whole journey.

  1. 6 km/h

  2. 12 km/h

  3. 5 km/h

  4. 8 km/h

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

The downstream speed of the boat is 9 + 3 = 12 km/h, and the upstream speed is 9 - 3 = 6 km/h. Since the distance traveled in both directions is equal, the average speed is given by the harmonic mean of the two speeds, which is 2 * 12 * 6 / (12 + 6) = 8 km/h.

Multiple choice

Amatya goes on a countryside trip where he can row a boat 30 km against the current and 45 km with the current in 10 hrs. Also, he can row 45 km against the current and 50 km with the current in 13 hrs. Find the rate of current and the speed of Amatya in still water (in km/hr).

  1. Rate of current- 2.5 km/hr, Speed of Amatya in still water- 5.75 km/hr

  2. Rate of current- 1.29 km/hr, Speed of Amatya in still water- 7.46 km/hr

  3. Rate of current- 1.5 km/hr, Speed of Amatya in still water- 8.5 km/hr

  4. Rate of current- 1.5 km/hr, Speed of Amatya in still water- 10 km/hr

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

Let x be boat speed and y be current speed. Equations: 30/(x-y) + 45/(x+y) = 10 and 45/(x-y) + 50/(x+y) = 13. Solving this system yields x = 7.46 and y = 1.29 approximately.