Boats & Streams
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Solved Examples
Study MaterialSolved Examples – Boats & Streams
Solved examples help students understand the practical application of Boats & Streams concepts in competitive examinations. These examples are designed from basic to advanced level and cover important problems frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, Defence, and placement aptitude tests.
Topics Covered in Solved Examples
- Downstream and Upstream Problems
- Boat Speed Calculations
- Stream Speed Problems
- Distance and Time Applications
- Average Speed Questions
- Ratio-Based Boat Problems
- Round Trip Problems
- Advanced Boats & Streams Applications
Example 1: Finding Downstream Speed
Question: The speed of a boat in still water is 12 km/h and the speed of the stream is 3 km/h. Find the downstream speed.
Solution:
Downstream speed:
= Boat speed + Stream speed
= 12 + 3
= 15 km/h
Therefore:
Downstream speed = 15 km/h
Example 2: Finding Upstream Speed
Question: The speed of a boat in still water is 20 km/h and the speed of the stream is 4 km/h. Find the upstream speed.
Solution:
Upstream speed:
= Boat speed − Stream speed
= 20 − 4
= 16 km/h
Therefore:
Upstream speed = 16 km/h
Example 3: Finding Boat Speed
Question: A boat moves downstream at 18 km/h and upstream at 10 km/h. Find the speed of the boat in still water.
Solution:
Boat speed:
= (Downstream speed + Upstream speed)/2
= (18 + 10)/2
= 28/2
= 14 km/h
Therefore:
Boat speed = 14 km/h
Example 4: Finding Stream Speed
Question: A boat moves downstream at 24 km/h and upstream at 16 km/h. Find the speed of the stream.
Solution:
Stream speed:
= (Downstream speed − Upstream speed)/2
= (24 − 16)/2
= 8/2
= 4 km/h
Therefore:
Stream speed = 4 km/h
Example 5: Downstream Time Problem
Question: A boat travels 60 km downstream in 3 hours. Find the downstream speed.
Solution:
Speed:
= Distance / Time
= 60/3
= 20 km/h
Therefore:
Downstream speed = 20 km/h
Example 6: Upstream Time Problem
Question: A boat travels 48 km upstream in 4 hours. Find the upstream speed.
Solution:
Speed:
= Distance / Time
= 48/4
= 12 km/h
Therefore:
Upstream speed = 12 km/h
Example 7: Finding Distance
Question: A boat moves downstream at 15 km/h for 4 hours. Find the distance travelled.
Solution:
Distance:
= Speed × Time
= 15 × 4
= 60 km
Therefore:
Distance travelled = 60 km
Example 8: Finding Time
Question: A boat travels 72 km upstream at 12 km/h. Find the time taken.
Solution:
Time:
= Distance / Speed
= 72/12
= 6 hours
Therefore:
Time taken = 6 hours
Example 9: Round Trip Problem
Question: A boat travels 30 km downstream and returns upstream. If downstream speed is 15 km/h and upstream speed is 10 km/h, find the total time taken.
Solution:
Downstream time:
= 30/15
= 2 hours
Upstream time:
= 30/10
= 3 hours
Total time:
= 2 + 3
= 5 hours
Therefore:
Total time taken = 5 hours
Example 10: Average Speed Problem
Question: A boat moves upstream at 8 km/h and downstream at 12 km/h. Find the average speed for equal distances.
Solution:
Average speed:
= 2xy / (x + y)
= (2 × 8 × 12)/(8 + 12)
= 192/20
= 9.6 km/h
Therefore:
Average speed = 9.6 km/h
Example 11: Ratio-Based Problem
Question: A boat takes 6 hours downstream and 9 hours upstream to cover the same distance. Find the ratio of downstream speed to upstream speed.
Solution:
For same distance:
Speed ratio:
= Inverse of time ratio
= 9 : 6
= 3 : 2
Therefore:
Required ratio = 3 : 2
Example 12: Finding Boat and Stream Speed Together
Question: Downstream speed is 20 km/h and upstream speed is 8 km/h. Find the speed of the boat and the stream.
Solution:
Boat speed:
= (20 + 8)/2
= 14 km/h
Stream speed:
= (20 − 8)/2
= 6 km/h
Therefore:
Boat speed = 14 km/h
Stream speed = 6 km/h
Example 13: Advanced Upstream-Downstream Problem
Question: A boat covers 56 km downstream in 4 hours and the same distance upstream in 7 hours. Find the speed of the boat in still water.
Solution:
Downstream speed:
= 56/4
= 14 km/h
Upstream speed:
= 56/7
= 8 km/h
Boat speed:
= (14 + 8)/2
= 11 km/h
Therefore:
Boat speed = 11 km/h
Example 14: Stream Speed Application
Question: A boat speed in still water is 18 km/h and downstream speed is 24 km/h. Find stream speed.
Solution:
Stream speed:
= Downstream speed − Boat speed
= 24 − 18
= 6 km/h
Therefore:
Stream speed = 6 km/h
Example 15: Advanced Round Trip Problem
Question: A boat travels 40 km downstream and 40 km upstream. If downstream speed is 20 km/h and upstream speed is 10 km/h, find the average speed for the entire journey.
Solution:
Total distance:
= 40 + 40
= 80 km
Downstream time:
= 40/20
= 2 hours
Upstream time:
= 40/10
= 4 hours
Total time:
= 2 + 4
= 6 hours
Average speed:
= 80/6
= 13.33 km/h
Therefore:
Average speed ≈ 13.33 km/h
Example 16: Equation Method Problem
Question: The speed of a boat in still water is twice the speed of the stream. If downstream speed is 18 km/h, find the speed of the boat.
Solution:
Let stream speed = x km/h
Boat speed = 2x km/h
Downstream speed:
= 2x + x
= 3x
3x = 18
x = 6
Boat speed:
= 2 × 6
= 12 km/h
Therefore:
Boat speed = 12 km/h
Important Exam Tips
- Always identify upstream and downstream correctly.
- Use addition for downstream problems.
- Use subtraction for upstream problems.
- Memorize all shortcut formulas.
- Use inverse ratio concept carefully.
- Simplify calculations early.
- Verify final answers properly.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving Boats & Streams questions in competitive examinations.