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
1. 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.2. 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.3. 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.4. 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.5. 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.6. 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.7. 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.8. 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.9. 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.10. 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
1. 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.2. 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.3. 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).4. 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.5. 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
