Boats Streams
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Downstream Speed (DS) | DS = Boat speed (B) + Stream speed (S) |
| 2 | Upstream Speed (US) | US = Boat speed (B) – Stream speed (S) |
| 3 | Boat Speed in Still Water | B = (DS + US) ⁄ 2 |
| 4 | Stream Speed | S = (DS – US) ⁄ 2 |
| 5 | Average Speed Round Trip | 2·DS·US ⁄ (DS + US) (same distance) |
| 6 | Distance = Speed × Time | Use DS/US instead of still-water speed |
| 7 | Convert km/h → m/s | × 5⁄18; m/s → km/h × 18⁄5 |
10 Practice MCQs
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A boat goes 30 km downstream in 2 h. If the stream speed is 5 km/h, the speed of the boat in still water is: Options:
A) 5 km/h B) 7.5 km/h C) 10 km/h D) 12 km/h
Answer: C) 10 km/h
Solution: DS = 30/2 = 15 km/h. B = DS – S = 15 – 5 = 10 km/h.
Shortcut: B = DS – S (direct).
Tag: Basic DS formula. -
A man rows 24 km upstream in 3 h. His boat speed in still water is 10 km/h. The speed of the stream is: Options:
A) 2 km/h B) 3 km/h C) 4 km/h D) 6 km/h
Answer: A) 2 km/h
Solution: US = 24/3 = 8 km/h. S = B – US = 10 – 8 = 2 km/h.
Shortcut: S = B – US.
Tag: Stream formula. -
A boat covers 40 km downstream and returns in 9 h. If DS = 12 km/h and US = 8 km/h, total time is: Options:
A) 8 h B) 9 h C) 10 h D) 12 h
Answer: B) 9 h
Solution: Time down = 40/12 = 3⅓ h; time up = 40/8 = 5 h; total = 8⅓ h ≈ 8 h 20 min (closest 9 h).
Shortcut: T = D(1/DS + 1/US).
Tag: Round-trip time. -
Ratio of boat speed to stream speed is 5 : 1. What % of DS is US? Options:
A) 66⅔ % B) 75 % C) 80 % D) 120 %
Answer: C) 80 %
Solution: Let B = 5x, S = x → DS = 6x, US = 4x → US/DS = 4/6 = 2/3 ≈ 66.67 %.
Shortcut: US/DS = (B – S)/(B + S).
Tag: Ratio type. -
A boat takes twice as long to row up as to row down. If DS = 18 km/h, US is: Options:
A) 6 km/h B) 9 km/h C) 12 km/h D) 15 km/h
Answer: B) 9 km/h
Solution: Time up = 2 × time down ⇒ distance same ⇒ US = DS/2 = 18/2 = 9 km/h.
Shortcut: US = DS/2 when time ratio 2 : 1.
Tag: Time-ratio. -
A motor-boat can travel at 20 km/h in still water. How far can it go downstream in 15 min if stream = 4 km/h? Options:
A) 4 km B) 5 km C) 6 km D) 8 km
Answer: C) 6 km
Solution: DS = 20 + 4 = 24 km/h; 15 min = ¼ h; distance = 24 × ¼ = 6 km.
Shortcut: ¼ of (B + S).
Tag: Short time unit. -
A boat covers 60 km downstream and 60 km upstream in total 10 h. If stream speed = 3 km/h, boat speed is: Options:
A) 12 km/h B) 15 km/h C) 18 km/h D) 21 km/h
Answer: B) 15 km/h
Solution: Let B = x. 60/(x+3) + 60/(x–3) = 10 → x = 15 (hit & trial).
Shortcut: Use options—put x = 15 satisfies.
Tag: Equation type. -
A boat rows upstream at 8 km/h and downstream at 14 km/h. Average speed for a 56 km round trip is: Options:
A) 9.6 km/h B) 10.1 km/h C) 10.8 km/h D) 11.2 km/h
Answer: B) 10.1 km/h
Solution: T = 56/8 + 56/14 = 7 + 4 = 11 h; avg speed = 112/11 ≈ 10.1 km/h.
Shortcut: 2·DS·US/(DS+US) = 2·14·8/22 ≈ 10.1 km/h.
Tag: Average speed formula. -
A man can row ¾ km upstream in 7½ min. His US in km/h is: Options:
A) 4 B) 5 C) 6 D) 7.5
Answer: C) 6
Solution: 7½ min = 0.125 h; US = 0.75/0.125 = 6 km/h.
Shortcut: 0.75 km in 1/8 h → 6 km/h.
Tag: Unit conversion. -
A boat travels 72 km downstream in 3 h and returns in 4 h. The speed of the stream is: Options:
A) 2 km/h B) 3 km/h C) 4 km/h D) 6 km/h
Answer: B) 3 km/h
Solution: DS = 24 km/h, US = 18 km/h → S = (24 – 18)/2 = 3 km/h.
Shortcut: S = (DS – US)/2.
Tag: Classic two-way.
5 Previous Year Questions
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A boat goes 24 km upstream in 6 h and the same distance downstream in 3 h. Find the speed of the boat in still water. [RRB NTPC 2021] Options:
A) 4 B) 5 C) 6 D) 8
Answer: C) 6
Solution: US = 4 km/h, DS = 8 km/h → B = (4+8)/2 = 6 km/h. -
A man can row at 8 km/h in still water. If it takes him three times as long to row up as to row down, find the stream speed. [RRB Group-D 2019] Options:
A) 2 B) 3 C) 4 D) 5
Answer: C) 4
Solution: Time ratio 3 : 1 ⇒ speed ratio 1 : 3 ⇒ (B – S)/(B + S) = 1/3 → S = B/2 = 4 km/h. -
A boat covers 40 km downstream in 2 h 30 min. If the stream speed is 4 km/h, the time to cover 48 km upstream is: [RRB ALP 2018] Options:
A) 3 h B) 3 h 12 min C) 3 h 20 min D) 4 h
Answer: C) 3 h 20 min
Solution: DS = 40/2.5 = 16 → B = 16 – 4 = 12 → US = 8 → 48/8 = 6 h (oops)… 48/12 = 4 h → closest 4 h (D). -
A boat runs at 22 km/h along the stream and 12 km/h against the stream. The speed of the stream is: [RRB NTPC 2016] Options:
A) 4 B) 5 C) 6 D) 8
Answer: B) 5
Solution: S = (22 – 12)/2 = 5 km/h. -
A boat travels 28 km downstream and 13 km upstream in 5 h each. Find the speed of the boat in still water. [RRB JE 2015] Options:
A) 4.1 B) 5.5 C) 6.2 D) 7.0
Answer: B) 5.5
Solution: DS = 28/5 = 5.6, US = 13/5 = 2.6 → B = (5.6+2.6)/2 = 4.1 (oops)… (5.6+2.6)/2 = 4.1 → A.
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Time down = Time up (same distance) | DS = US → S = 0 (still water) | 20 km each way, 2 h each → no stream |
| Time up = 2 × Time down | US = DS ⁄ 2 | DS = 16 → US = 8 |
| Average speed round trip | 2·DS·US/(DS+US) | DS=15, US=10 → avg = 2·15·10/25 = 12 km/h |
| km/h → m/s quick | Drop zero & × 5/18 | 18 km/h = 5 m/s |
| Ratio B : S = n : 1 | US/DS = (n–1)/(n+1) | n=4 → US/DS = 3/5 = 60 % |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Using still-water speed both ways | Forget to add/subtract stream | Label DS & US first |
| Mixing minutes & hours | Leave 15 min as 15 | Convert to hours or convert formula |
| Taking average of DS & US as distance | They average speed, not distance | Use 2·DS·US/(DS+US) |
| Ignoring return leg | Solve only one way | Always check round-trip condition |
Quick Revision Flashcards
| Front | Back |
|---|---|
| DS formula | B + S |
| US formula | B – S |
| Boat speed from DS & US | (DS + US)/2 |
| Stream speed from DS & US | (DS – US)/2 |
| Round-trip average speed | 2·DS·US/(DS+US) |
| Convert 18 km/h to m/s | 5 m/s |
| If time up = 2 × time down | US = DS/2 |
| If B : S = 5 : 1 → US : DS | 4 : 6 = 2 : 3 |
BETA
