1. Basic relations
Boat speed in still water = b, stream speed = s.
- Downstream (with the current): D = b + s
- Upstream (against the current): U = b − s
- b = (D + U)/2, s = (D − U)/2
2. Standard results
- Going d km and coming back: total time = d/(b + s) + d/(b − s) = 2bd/(b² − s²).
- If upstream takes k times as long as downstream for the same distance: b : s = (k + 1) : (k − 1).
- Average speed for a round trip = (b + s)(b − s)/b = (b² − s²)/b — always less than b.
- If a man takes T hours for a round trip, distance = T(b² − s²)/(2b).
3. Solved examples
b = 10 km/h, s = 2 km/h. 24 km downstream: 24/12 = 2 h; back: 24/8 = 3 h; total 5 h.
Downstream 12 km/h, upstream 8 km/h → b = 10, s = 2 km/h.
A man rows 30 km downstream in 3 h and 18 km upstream in 3 h → D = 10, U = 6 → b = 8, s = 2.
Upstream takes twice as long → b : s = 3 : 1. If b = 9, s = 3 km/h.
b = 5, s = 1, round trip takes 1 h. d = 1 × (25 − 1)/(2 × 5) = 2.4 km.
A boat covers 24 km downstream in the same time as 16 km upstream; s = 2. (b + 2)/(b − 2) = 3/2 → b = 10 km/h.
4. Traps
- "Speed of the man" usually means speed in still water.
- Convert minutes to hours before dividing.
- Rafts and logs float at stream speed (b = 0).
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. A boat goes at 13 km/h in still water. The stream flows at 1 km/h. Time taken to go 96 km upstream is:
(a) 8 hours (b) 6 6/7 hours (c) 7 5/13 hours (d) 9 hours
Answer: (a) 8 hours
Solution: Upstream speed = 13 − 1 = 12 km/h. Time = 96/12 = 8 hours.
ASO exam level
Example 2. A man rows 33 km downstream in 3 hours and 12 km upstream in 4 hours. The speed of the stream is:
(a) 7 km/h (b) 4 km/h (c) 7/2 km/h (d) 5 km/h
Answer: (b) 4 km/h
Solution: Down = 11, up = 3 km/h. Stream = (11 − 3)/2 = 4 km/h (still water 7 km/h).
Example 3. A man takes 4 times as long to row a distance upstream as to row the same distance downstream. The ratio of the speed of the boat in still water to the speed of the stream is:
(a) 5 : 1 (b) 5 : 3 (c) 4 : 1 (d) 3 : 5
Answer: (b) 5 : 3
Solution: (b + s)/(b − s) = 4 → b/s = (4 + 1)/(4 − 1) = 5 : 3.
Example 4. A boat whose speed in still water is 13 km/h goes downstream and comes back in 26 hours. If the stream flows at 5 km/h, the distance one way is:
(a) 144 km (b) 288 km (c) 157 km (d) 169 km
Answer: (a) 144 km
Solution: Time = D/18 + D/8 = D × 26/144 = 26 → D = 144 km.
Example 5. A boat's speed in still water is 12 km/h and the stream flows at 3 km/h. How long will it take to go 36 km downstream and come back?
(a) 6 h (b) 4 h (c) 6 h 24 min (d) 7 h 24 min
Answer: (c) 6 h 24 min
Solution: Downstream 15 km/h → 2.4 h; upstream 9 km/h → 4 h. Total = 6 h 24 min.
Example 6. A boat's speed in still water is 10 km/h and the stream flows at 2 km/h. How long will it take to go 36 km downstream and come back?
(a) 7 h 30 min (b) 8 h 30 min (c) 4 h 30 min (d) 7 h 12 min
Answer: (a) 7 h 30 min
Solution: Downstream 12 km/h → 3 h; upstream 8 km/h → 4.5 h. Total = 7 h 30 min.
Example 7. A man rows downstream at 15 km/h and upstream at 9 km/h. His speed in still water and the speed of the stream are:
(a) 12 km/h and 3 km/h (b) 3 km/h and 12 km/h (c) 13 km/h and 2 km/h (d) 15 km/h and 9 km/h
Answer: (a) 12 km/h and 3 km/h
Solution: Still water = (down + up)/2 = 12 km/h. Stream = (down − up)/2 = 3 km/h.
Advanced level
Example 8. A boat covers 36 km downstream in the same time as 12 km upstream. If the stream flows at 4 km/h, the speed of the boat in still water is:
(a) 9 km/h (b) 12 km/h (c) 8 km/h (d) 4 km/h
Answer: (c) 8 km/h
Solution: (8 + 4)/(8 − 4) = 36/12: check with b = 8: down 12, up 4, ratio 3 : 1 ✓. Solve: 36(b − 4) = 12(b + 4) → b = 8 km/h.
Example 9. A boat covers 42 km downstream in the same time as 36 km upstream. If the stream flows at 1 km/h, the speed of the boat in still water is:
(a) 14 km/h (b) 12 km/h (c) 15 km/h (d) 13 km/h
Answer: (d) 13 km/h
Solution: (13 + 1)/(13 − 1) = 42/36: check with b = 13: down 14, up 12, ratio 7 : 6 ✓. Solve: 42(b − 1) = 36(b + 1) → b = 13 km/h.
Example 10. A man takes 2 times as long to row upstream as to row the same distance downstream. If his speed in still water is 9 km/h, the speed of the stream is:
(a) 3 km/h (b) 4 km/h (c) 4.5 km/h (d) 27 km/h
Answer: (a) 3 km/h
Solution: (b + s)/(b − s) = 2 → s = b(2 − 1)/(2 + 1) = 3 km/h.
Topic-wise practice for Boats and streams (Quant): Upstream and downstream. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- Upstream and downstream speed
- Speed of the boat and stream
- Time to go and return
- Distance from total time