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 takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

  1. 2mph

  2. 2.5mph

  3. 3mph

  4. 3.2mph

  5. 3.5mph
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let s be the speed of the stream. Downstream speed = 10+s, upstream = 10-s. Time difference = 36/(10-s) - 36/(10+s) = 1.5 hours (90 mins). 36(10+s - (10-s)) / (100-s^2) = 1.5 => 72s / (100-s^2) = 1.5 => 48s = 100 - s^2 => s^2 + 48s - 100 = 0. Solving gives (s+50)(s-2) = 0. Speed s = 2 mph.

Multiple choice

Priya and Neeraj can row a boat at 12 km/h and 16 km/h, respectively, in still water. In a river flowing with a constant velocity, Neeraj takes 1 hour more to row 30 km upstream than to row the same distance downstream. If Priya starts from a certain point in the river, rows downstream to some location, and then immediately returns upstream to the same starting point, taking a total of 90 minutes, what is the total distance, in km, that Priya will cover?

  1. 4

  2. 8

  3. 12

  4. 16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let river speed be v. Neeraj: 30/(16-v) - 30/(16+v) = 1. Solving gives v=4. Priya: 12 km/h, downstream speed 16, upstream 8. Time = d/16 + d/8 = 1.5 hours. 3d/16 = 1.5, d = 8. Total distance = 2d = 16.

Multiple choice

Passage

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 of these quantities.

Quantity I: Speed of boat in still water, if a man can travel 48 km downstream in 8 hours and 80 km upstream in 20 hours. Quantity II: Speed of boat in still water, if a man can travel 25 km downstream in 5 hours and the speed of stream, is 1 kmph.

  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
A Correct answer
Explanation

Q1: Downstream speed = 48/8 = 6 kmph. Upstream speed = 80/20 = 4 kmph. Still water speed = (6+4)/2 = 5 kmph. Q2: Downstream speed = 25/5 = 5 kmph. Stream speed = 1 kmph. Still water speed = 5 - 1 = 4 kmph. Q1 > Q2.

Multiple choice

Passage

In each of the following questions, a question & then two statements – I & II are given. You have to determine that the data provided in these statements is enough to answer the question or not. Study both the statement: निम्नलिखित प्रत्येक प्रश्न में एक प्रश्न और फिर दो कथन I और II दिए गए हैं। आपको यह निर्धारित करना है कि इन कथनों में प्रदान किया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों का अध्ययन करें:

A boat takes 4 hours to go upstream from A to B and back downstream from B to A in a river. What is the speed of the boat in still water? एक नाव एक नदी में A से B तक और धारा के अनुकूल B से A तक वापस जाने में 4 घंटे का समय लेती है। शांत जल में नाव की गति क्या है? Statement I : The distance between A and B is 12 km. The boat takes 2 hours less to go downstream than upstream. Statement II : The boat takes 2 hours less to go downstream than upstream and the speed of the water current is 2 km / h. कथन I: A और B के बीच की दूरी 12 किमी है। नाव धारा के प्रतिकूल जाने की अपेक्षा धारा के अनुकूल जाने में 2 घंटे कम समय लेती है। कथन II: नाव को धारा के प्रतिकूल जाने में 2 घंटे कम समय लगता है और पानी की धारा की गति 2 किमी / घंटा है।

  1. Only Statement I alone. केवल कथन I

  2. Only Statement II alone. केवल कथन II

  3. Both Statements I and II together. दोनों कथन I और II एक साथ

  4. Neither Statement I nor II is sufficient. न तो कथन I और न ही II पर्याप्त है।

  5. Either Statement I or II. या तो कथन I या II
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For Statement I: Total time = 4 hours, downstream takes 2 hours less than upstream. So upstream time = 3 hours, downstream time = 1 hour. Distance = 12 km. Upstream speed = 12/3 = 4 km/h (boat - current), downstream speed = 12/1 = 12 km/h (boat + current). Adding gives 2×boat = 16, so boat speed = 8 km/h. Statement I alone is sufficient. For Statement II: Same time logic gives upstream = 3 hours, downstream = 1 hour. Let distance = d, boat = b, current = 2 km/h. Then d/(b+2) = 1 and d/(b-2) = 3. Solving gives b = 8 km/h. Statement II alone is also sufficient. Therefore either statement alone is sufficient.

Multiple choice

Passage

Read the following information and answer the given questions- Day 1: Ram covers 200 km along the stream and 150 km against the stream. The difference between the time taken to cover upstream and downstream is 10 hours. Day 2: Ram covers 40 km less than the previous day in along the stream and distance covered against the stream is equal to the distance covered by Ram in day 3 along the stream. Time taken to cover downstream distance is 8 hours less than the upstream distance. Day 3: Distance covered along the stream is 40 km more than the distance covered against the stream which is equal to the distance covered by Ram on day 1 along the stream. He takes 6 hours more to cover upstream than the downstream distance. Day 4: Time taken to covers 200 km along the stream and 100 km against the stream is same as the total time taken by Ram on day 3. The speed of stream on day 1, 2, 3 and 4 is 15kmph, 10 kmph, 20 kmph and 20 kmph respectively.

Sum of the speed of boats on day 2 and day 3 together is what percentage more or less than the sum of the speed of stream on day 1 and day 4 together?

  1. 120

  2. 160

  3. 100

  4. 200

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

This involves calculating boat speeds on days 2 and 3, stream speeds on days 1 and 4, then computing percentage difference. The result 100 indicates the sum of boat speeds is exactly equal to the sum of stream speeds - meaning 0% difference, but expressed as the base value 100.

Multiple choice

Passage

The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

What is the speed of boat in still water? Statement I:. The boat can cover 25 km downstream distance in 5 hours. Statement II: Speed of the stream is two-third of the speed of boat in still water. Statement III: The boat can cover 25 km upstream distance in 10 hours.

  1. I and III together

  2. Only II

  3. I and II together

  4. I and either II or III

  5. Any two statements together
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Downstream speed = boat + stream. Upstream speed = boat - stream. Statement I: downstream speed = 25/5 = 5 km/h. Statement III: upstream speed = 25/10 = 2.5 km/h. Statement II: stream = (2/3) × boat. Combining I and III: boat = (5 + 2.5)/2 = 3.75 km/h. Combining I and II: 5 = boat + (2/3)boat, so boat = 3 km/h. Any two statements together are sufficient. Option E is correct.

Multiple choice

Passage

Directions: Read the following information and answer the question that follows: Arjun can beat Amit by 15 metres in a 100-m race, whereas Ravi is 20% slower than Amit. Ashwani, whose speed is 3 m/sec, beats Arjun by 15 seconds in a 150-m race. If Ashwani and Ravi run a 100-m race, Ashwani beats Ravi by x metres.

If the downstream time of boat is x% less than upstream time of boat, then the speed of boat is what percent more than speed of stream?

  1. 209.2%

  2. 219.3%

  3. 228.4%

  4. 237.5%

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