Boats and Streams
Boats and Streams
A boat moving with the current (downstream) gains the stream's speed; moving against it (upstream) loses it. Two equations, two unknowns: that is the whole topic. NTPC asks speeds from downstream and upstream data, round trips, "upstream takes k times as long", and two-trip equations.
1. Formula Box
Downstream speed D = b + s Upstream speed U = b − s
Boat in still water b = (D + U)/2 Stream s = (D − U)/2
Upstream time k times downstream time (same distance): (b + s) = k(b − s), so b : s = (k + 1) : (k − 1)
Round trip of distance d: time = d/(b + s) + d/(b − s)
| D | U | b | s |
|---|---|---|---|
| 18 | 12 | 15 | 3 |
| 15 | 7 | 11 | 4 |
| 37 | 23 | 30 | 7 |
✗ Downstream 18, upstream 12, so stream speed 6 | ✓ Stream = (18 − 12)/2 = 3; the difference is twice the stream speed
✗ Upstream takes twice as long, so b = 2s | ✓ (b + s) = 2(b − s) gives b = 3s
हिंदी नोट: धारा के साथ (अनुप्रवाह) चाल = नाव + धारा, धारा के विरुद्ध (ऊर्ध्वप्रवाह) चाल = नाव − धारा। नाव की चाल = दोनों चालों का योग ÷ 2, धारा की चाल = अंतर ÷ 2।
Exam Pointer: Verified NTPC patterns: boat and stream speeds from downstream and upstream data (January 2021, June 2025 Graduate CBT-1), upstream time a multiple of downstream time (April 2016) and two mixed down-up trips solved as equations (June 2022 CBT-2). The plain round-trip time had no verified NTPC shift and is tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Boat and stream speeds from downstream and upstream
[PYQ: NTPC CBT-1 9-Jan-2021 Shift-1 | NTPC Graduate CBT-1 12-Jun-2025 Shift-2]
EXAM LEVEL
Q. A boat goes downstream at 18 km/h and upstream at 12 km/h. Find its speed in still water and the stream's speed.
b = (18 + 12)/2 = 15 km/h, s = (18 − 12)/2 = 3 km/h.
Answer: 15 km/h and 3 km/h
EXAMATLAS LEVEL
Q. A boat covers 30 km downstream in 2 hours and 21 km upstream in 3 hours. Find the speeds of the boat and the stream.
D = 15 km/h and U = 7 km/h, so b = 11 km/h and s = 4 km/h.
Answer: Boat 11 km/h, stream 4 km/h
Pattern 2: Round trip time
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. 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 48 km downstream and come back?
48/12 + 48/8 = 4 + 6 = 10 hours.
Answer: 10 hours
EXAMATLAS LEVEL
Q. A man rows to a place 24 km away and back in 9 hours. The stream flows at 2 km/h. Find his rowing speed in still water.
24/(b + 2) + 24/(b − 2) = 9. Testing values (the answer must exceed 2): b = 6 gives 24/8 + 24/4 = 3 + 6 = 9. So b = 6 km/h.
Answer: 6 km/h
Pattern 3: Upstream takes k times as long as downstream
[PYQ: NTPC CBT-1 27-Apr-2016 Shift-1]
EXAM LEVEL
Q. A man takes twice as long to row a distance upstream as downstream. Find the ratio of his speed in still water to the stream's speed.
b + s = 2(b − s), so b = 3s and the ratio is 3 : 1. Formula: (k + 1) : (k − 1) = 3 : 1.
Answer: 3 : 1
EXAMATLAS LEVEL
Q. A boat's speed in still water is 12 km/h, and it takes 3 times as long upstream as downstream. Find the stream's speed and the time to go 36 km downstream and come back.
12 + s = 3(12 − s), so 4s = 24 and s = 6 km/h. D = 18, U = 6. Round trip = 36/18 + 36/6 = 2 + 6 = 8 hours.
Answer: 6 km/h; 8 hours
Pattern 4: Two mixed trips solved as equations
[PYQ: NTPC CBT-2 14-Jun-2022 Shift-1]
EXAM LEVEL
Q. A boat goes 24 km downstream and 20 km upstream in 4.5 hours, and 36 km downstream and 16 km upstream in 5 hours. Find the speeds of the boat and the stream.
Let x = 1/D and y = 1/U: 24x + 20y = 4.5 and 36x + 16y = 5. Solving, x = 1/12 and y = 1/8, so D = 12 and U = 8. Boat 10 km/h, stream 2 km/h.
Answer: 10 km/h and 2 km/h
EXAMATLAS LEVEL
Q. A boat goes 30 km downstream and 21 km upstream in 5 hours, and 45 km downstream and 14 km upstream in 5 hours. Find its speeds and the time to go 60 km downstream and return.
30x + 21y = 5 and 45x + 14y = 5. Doubling the first and tripling the second: 60x + 42y = 10 and 135x + 42y = 15, so 75x = 5, x = 1/15 and D = 15; then 21y = 3, y = 1/7 and U = 7. Boat 11, stream 4. Round trip = 60/15 + 60/7 = 4 + 8 4/7 = 12 4/7 hours.
Answer: Boat 11 km/h, stream 4 km/h; 12 4/7 hours
60-Second Revision
- D = b + s, U = b − s; b = (D + U)/2, s = (D − U)/2.
- Upstream k times as long: b : s = (k + 1) : (k − 1).
- Round trip = d/D + d/U.
- Two trips: set x = 1/D, y = 1/U and solve two linear equations.