In this guide
Boats and streams is a special case of time, speed and distance. The only new idea is that the water itself moves. Going with the current, the river carries the boat along; going against it, the boat has to fight the flow.
NTPC questions on this topic are usually short: find a speed, find a time, or find a distance from a round-trip time. The traps are in the reading, not in the arithmetic.
The two speeds
Let the boat's speed in still water be b and the stream's speed be s.
| Direction | Effective speed |
|---|---|
| Downstream (with the current) | D = b + s |
| Upstream (against the current) | U = b − s |
Why: in still water the boat covers b km each hour. The river moves the whole body of water s km each hour. Going downstream, the two movements add up; going upstream, the river takes back s km of every b the boat rows.
"Speed of a person rowing in still water" means the same as the boat's speed b.
Going back from D and U
If the question gives downstream and upstream speeds, add and subtract:
- Boat's speed in still water: b = (D + U) ÷ 2
- Stream's speed: s = (D − U) ÷ 2
Why: D + U = (b + s) + (b − s) = 2b, and D − U = 2s. This is just solving two simultaneous equations in one step.
If the question gives distances and times, find D and U first by dividing distance by time.
Round trips
A boat goes d km downstream and comes back the same d km upstream.
- Total time = d/(b + s) + d/(b − s) = 2bd ÷ (b² − s²)
- Average speed for the round trip = 2DU ÷ (D + U), the same equal-distance rule as in speed questions.
The round trip always takes longer than it would in still water, because the boat spends more time on the slow upstream leg than it saves on the fast downstream leg.
The time-ratio shortcut
If going upstream takes n times as long as going downstream over the same distance, then:
b : s = (n + 1) : (n − 1)
Why: for a fixed distance, time is inversely proportional to speed. So D : U = n : 1. Adding and halving gives b ∝ (n + 1) and s ∝ (n − 1).
For example, if upstream takes twice as long, b : s = 3 : 1.
Summary table
| Given | Find | Use |
|---|---|---|
| b and s | Speeds on the river | D = b + s, U = b − s |
| D and U | b and s | Half the sum, half the difference |
| Distances and times | D and U | Distance ÷ time for each leg |
| Time ratio n : 1 | b : s | (n + 1) : (n − 1) |
| b, s and round-trip time | Distance | d/D + d/U = total time |
Worked questions at NTPC level
Q1. A boat's downstream speed is 15 km/h and upstream speed is 9 km/h. Find the speeds of the boat and the stream.
Boat = (15 + 9) ÷ 2 = 12 km/h.
Stream = (15 − 9) ÷ 2 = 3 km/h.
Q2. A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. How long does it take to go 24 km downstream and come back?
D = 12 km/h: 24 ÷ 12 = 2 h. U = 8 km/h: 24 ÷ 8 = 3 h.
Total = 5 hours.
Q3. A person rows 30 km downstream in 3 hours and 18 km upstream in 3 hours. Find the speeds of the boat and the stream.
D = 10 km/h, U = 6 km/h.
Boat = 8 km/h; stream = 2 km/h.
Q4. Rowing upstream takes twice as long as rowing downstream over the same distance. The boat's speed in still water is 12 km/h. Find the stream's speed.
b : s = (2 + 1) : (2 − 1) = 3 : 1, so s = 12 ÷ 3 = 4 km/h.
Check: D = 16, U = 8, and 8 is half of 16.
Q5. A person can row at 6 km/h in still water. The river flows at 2 km/h. It takes 3 hours to row to a place and back. How far is the place?
D = 8, U = 4. So d/8 + d/4 = 3, which gives 3d/8 = 3.
d = 8 km. Check: 1 h down + 2 h up = 3 h.
Q6. A boat with a still-water speed of 5 km/h goes 24 km downstream and returns in 10 hours. Find the stream's speed.
Total time = 2 × 5 × 24 ÷ (25 − s²) = 240 ÷ (25 − s²) = 10.
So 25 − s² = 24, and s = 1 km/h.
Check: 24 ÷ 6 + 24 ÷ 4 = 4 + 6 = 10 hours. Testing options is just as fast here.
Common mistakes
- Adding the stream when going upstream. Upstream is always b − s.
- Using the still-water speed for a journey. Journeys on a river use D or U, never b alone.
- Answering the wrong speed. Underline whether the question wants the boat, the stream, D or U.
- Averaging D and U for a round trip. Use total distance ÷ total time.
Practice set
- Downstream speed is 20 km/h and upstream speed is 12 km/h. Find the speeds of the boat and the stream.
- A boat's still-water speed is 8 km/h and the stream flows at 2 km/h. How long does it take to go 30 km downstream?
- With the same boat and stream, how long does 30 km upstream take?
- A person rows 36 km downstream in 4 hours and 24 km upstream in 4 hours. Find the speeds of the boat and the stream.
- A boat goes at 9 km/h in still water and the stream flows at 3 km/h. How long does a round trip of 12 km each way take?
- Going upstream takes three times as long as going downstream over the same distance. Find the ratio of the boat's speed to the stream's speed.
- A person rows at 5 km/h in still water; the stream flows at 1 km/h. The trip to a place and back takes 5 hours. How far is the place?
- A boat goes 45 km downstream in 3 hours. The stream flows at 3 km/h. How long will 45 km upstream take?
Answers:
- Boat 16 km/h, stream 4 km/h. Half of 32 and half of 8.
- 3 hours. 30 ÷ 10.
- 5 hours. 30 ÷ 6.
- Boat 7.5 km/h, stream 1.5 km/h. D = 9, U = 6.
- 3 hours. 12 ÷ 12 + 12 ÷ 6 = 1 + 2.
- 2 : 1. (3 + 1) : (3 − 1) = 4 : 2.
- 12 km. d/6 + d/4 = 5, so 5d/12 = 5.
- 5 hours. D = 15, so b = 12 and U = 9; 45 ÷ 9.
What to do next
- Write D = b + s and U = b − s at the top of your rough sheet until you no longer need to.
- Solve 15 questions, labelling each one by the row of the summary table it uses.
- Try five round-trip questions by testing options instead of forming the equation, and time yourself.
- Revise problems on trains, which uses the same relative-speed idea.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Railway Recruitment Boards website .
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