Boats and Streams Notes for SSC Exams

Boats and Streams is a short and scoring chapter of SSC Quantitative Aptitude. A boat moves with or against the water of a river, and we find speeds, times or distances. These boats and streams notes for SSC explain all the formulas with simple examples and practice questions.

Basic Terms

• Still water speed (u): the speed of the boat in calm water.
• Stream speed (v): the speed of the river's flow.
• Downstream: the boat moves in the direction of the stream.
• Upstream: the boat moves against the stream.

Important Formulas

Round Trips and Equal Distance

In a round trip the boat covers the same distance downstream and upstream, so the average speed is not the simple average of the two speeds. Use the formula for the harmonic mean: 2DU / (D + U), which is the same as (u squared - v squared) / u.

Ratio of Times

For the same distance, the times taken downstream and upstream are in the inverse ratio of the speeds. If a boat takes twice as long upstream as downstream, then (u + v) / (u - v) = 2, so u = 3v, i.e. the boat speed is 3 times the stream speed.

Solved Examples

Example 1: The speed of a boat in still water is 10 km/h and the speed of the stream is 2 km/h. Find the downstream and upstream speeds.
Solution: Downstream = 10 + 2 = 12 km/h. Upstream = 10 - 2 = 8 km/h.

Example 2: A boat goes downstream at 15 km/h and upstream at 9 km/h. Find the speed of the boat and the stream.
Solution: Boat = (15 + 9) / 2 = 12 km/h. Stream = (15 - 9) / 2 = 3 km/h.

Example 3: A boat can row at 8 km/h in still water. The speed of the stream is 2 km/h. How long will it take to go 30 km downstream?
Solution: Downstream speed = 10 km/h. Time = 30 / 10 = 3 hours.

Example 4: A man rows 30 km upstream in 3 hours and the same distance downstream in 2 hours. Find the speed of the man in still water and of the stream.
Solution: Upstream = 10 km/h, downstream = 15 km/h. Man = 12.5 km/h and stream = 2.5 km/h.

Example 5: A boat's speed in still water is 10 km/h and the stream speed is 2 km/h. It goes 24 km downstream and returns. Find the total time.
Solution: Time = 24/12 + 24/8 = 2 + 3 = 5 hours.

Example 6: A boat goes 20 km downstream in 2 hours and returns in 4 hours. Find the speed of the boat in still water.
Solution: Downstream = 10 km/h, upstream = 5 km/h. Boat = (10 + 5) / 2 = 7.5 km/h.

Quick Tips to Solve Faster

• Always find the downstream and upstream speeds first.
• Boat speed is the average of the two speeds, and stream speed is half their difference.
• For a round trip, add the times separately instead of averaging the speeds.
• If the upstream time is double, the boat speed is 3 times the stream speed.
• Convert time into hours if the speed is in km/h.

Common Mistakes to Avoid

• Taking the speed of the boat as the downstream speed.
• Using the simple average for the average speed in a round trip.
• Forgetting to halve while finding the speeds from D and U.
• Mixing up the upstream and downstream directions.
• Not converting minutes into hours.

Quick Revision Points

• Downstream = u + v and upstream = u - v.
• u = (D + U) / 2 and v = (D - U) / 2.
• Average round-trip speed = (u squared - v squared) / u.
• Upstream time n times downstream: u : v = (n + 1) : (n - 1).
• Time = Distance / Speed.

Practice Questions With Answers

1. A boat has a speed of 12 km/h in still water and the stream flows at 3 km/h. Find the upstream speed.
   Answer: 9 km/h (12 - 3).
2. A boat goes downstream at 18 km/h and upstream at 10 km/h. Find the speed of the stream.
   Answer: 4 km/h ((18 - 10) / 2).
3. A boat with a speed of 9 km/h in still water goes 36 km downstream in a stream of 3 km/h. Find the time.
   Answer: 3 hours (36 / 12).
4. A boat with a speed of 15 km/h in still water goes 60 km upstream in a stream of 5 km/h. Find the time.
   Answer: 6 hours (60 / 10).
5. The downstream speed is 8 km/h and the upstream speed is 4 km/h. Find the speed of the boat in still water.
   Answer: 6 km/h ((8 + 4) / 2).
6. A boat takes twice as long to go upstream as downstream. Find the ratio of the boat speed to the stream speed.
   Answer: 3 : 1 ((u + v) / (u - v) = 2).
7. A boat with a speed of 6 km/h in still water in a stream of 2 km/h goes 8 km downstream and returns. Find the total time.
   Answer: 3 hours (8/8 + 8/4).
8. A boat has a speed of 20 km/h in still water and the stream is 4 km/h. Find the average speed for a round trip.
   Answer: 19.2 km/h ((400 - 16) / 20).
9. The downstream speed is 12 km/h and the upstream speed is 6 km/h. Find the speed of the stream.
   Answer: 3 km/h ((12 - 6) / 2).
10. A boat with a speed of 7.5 km/h in still water in a 2.5 km/h stream goes 25 km downstream. Find the time.
    Answer: 2.5 hours (25 / 10).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC boats and streams practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Speed, Distance and Time Notes
• Time and Work Notes
• Pipes and Cisterns Notes
• Ratio and Proportion Notes
• SSC Boats and Streams Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is the formula for downstream speed?

Downstream speed = speed of the boat in still water + speed of the stream.

What is the formula for upstream speed?

Upstream speed = speed of the boat in still water - speed of the stream.

How many questions come from boats and streams in SSC exams?

Usually one question comes from this chapter in SSC CGL and CHSL Tier 1.

How do I find the speed of the boat in still water?

It is half the sum of the downstream and upstream speeds.

How do I find the speed of the stream?

It is half the difference of the downstream and upstream speeds.

What is the average speed in a round trip?

It is (u squared - v squared) / u, where u is the boat speed and v is the stream speed.

Is boats and streams related to speed and distance?

Yes. It uses the same formula, Speed = Distance / Time, with the speeds changed by the stream.

How should I practise boats and streams?

Learn the formulas, solve the examples here and then attempt the boats and streams practice paper.