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 motor boat whose speed is $18$ km/h in still water takes $1$hour more to go $24$ km upstream than to return downstream to the same spot. The speed of the stream is
  1. $6$ km/hr
  2. $5$ km/hr
  3. $3.5$ km/hr
  4. $4.5$ km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be the stream speed. Upstream speed is 18-v, downstream is 18+v. Time difference is 24/(18-v) - 24/(18+v) = 1. Solving 24(18+v - 18+v) / (324 - v^2) = 1 gives 48v = 324 - v^2, or v^2 + 48v - 324 = 0. Factoring (v+54)(v-6) = 0 gives v = 6.

Multiple choice

A man can row a boat with $4 km/h$ in still water. If he is crossing a river where the current is $2 km/h$ and width of river is $4 km$. How long will it take him to row $2 km$ up the stream and then back to his starting point?
  1. $2 hrs$
  2. $1 hr$
  3. $\dfrac{4}{3} hrs$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Upstream speed = 4 - 2 = 2 km/h. Downstream speed = 4 + 2 = 6 km/h. Time upstream = 2 km / 2 km/h = 1 hour. Time downstream = 2 km / 6 km/h = 1/3 hour. Total time = 1 + 1/3 = 4/3 hours.

Multiple choice

The speed of a boat in still water is $11$ km/hr and the speed of the stream is $x$ km/hr. Find in terms of $x$, the speed of boat upstream and the speed of boat downstream. If the boat takes $\displaystyle 2\frac{3}{4}$ hours to go 12 km upstream and then return, find the value of $x$.
  1. $1$
  2. $5$
  3. $9$
  4. $13$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Upstream speed = 11-x, downstream = 11+x. Time = 12/(11-x) + 12/(11+x) = 11/4. Solving for x: 12(11+x+11-x)/(121-x^2) = 11/4. 12(22)/(121-x^2) = 11/4. 264/(121-x^2) = 11/4. 24/(121-x^2) = 1/4. 96 = 121-x^2. x^2 = 25, x = 5.

Multiple choice

A motor boat whose speed is 15 km/hr in still water goes 40 km downstream and comes back in a total of 6 hours. The speed of the stream is

  1. 9 km/hr

  2. 7 km/hr

  3. 5 km/hr

  4. 3 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let stream speed be s. Downstream speed = 15 + s, upstream speed = 15 - s. Total time = 40 / (15 + s) + 40 / (15 - s) = 6. 40 * (15 - s + 15 + s) / (225 - s^2) = 6. 40 * 30 / (225 - s^2) = 6. 1200 / (225 - s^2) = 6. 200 = 225 - s^2. s^2 = 25, so s = 5.

Multiple choice

A motor boat whose speed is $15$ km/hr in still water goes $30$ km downstream and comes back in $4$ hours $30$ minutes. Determine the speed of the stream.
  1. $12$ km/hr
  2. $9$ km/hr
  3. $5$ km/hr
  4. $3$ km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the stream speed be x. The downstream speed is 15+x and upstream is 15-x. The total time is 30/(15+x) + 30/(15-x) = 4.5. Solving this quadratic equation 30(15-x + 15+x) / (225-x^2) = 4.5 leads to 900 / (225-x^2) = 4.5, so 225-x^2 = 200, x^2 = 25, x = 5.

Multiple choice

A boat has a speed of $15$m/hr in still water. In a stream that has a current of $5$ m/hr it travels a certain distance downstream and returns. The ratio of the average speed for the round trip to the speed in still water is:
  1. $\dfrac{5}{4}$
  2. $\dfrac{1}{5}$
  3. $\dfrac{8}{9}$
  4. $\dfrac{7}{8}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be d. Downstream speed = 15 + 5 = 20. Upstream speed = 15 - 5 = 10. Average speed = 2 * 20 * 10 / (20 + 10) = 400 / 30 = 40/3. Ratio to speed in still water (15) = (40/3) / 15 = 40/45 = 8/9.

Multiple choice

Rekha can row her boat at the speed of $5$ km/hr in still water. If it takes one hour more to row the boat $5.25$ km upstream than to return downstream. Find the speed of the stream.
  1. $9$ km/hr
  2. $5$ km/hr
  3. $2$ km/hr

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed of stream be s. Upstream speed = 5-s, downstream speed = 5+s. Time difference: 5.25/(5-s) - 5.25/(5+s) = 1. 5.25 * (5+s - (5-s)) / (25-s^2) = 1. 5.25 * 2s = 25-s^2. 10.5s = 25-s^2. s^2 + 10.5s - 25 = 0. Using quadratic formula: s = (-10.5 + sqrt(110.25 + 100)) / 2 = (-10.5 + 14.5) / 2 = 2.

Multiple choice

The speed of a motorboat is to that of the current of water as $36 : 5$. The boat goes along with the current in $5$ hours $10$ min. It will come back in
  1. $5$ hours $50$ min
  2. $6$ hours
  3. $6$ hours $50$ min
  4. $12$ hours $10$ min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = 36x, current = 5x. Downstream speed = 41x, upstream = 31x. Time downstream = 5h 10m = 310 min. Distance = 41x * 310. Time upstream = Distance / 31x = (41x * 310) / 31x = 41 * 10 = 410 min. 410 min = 6 hours 50 min.