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Boats and Streams (Upstream / Downstream)

Introduction

Boats and Streams पर आधारित questions यह परखते हैं कि नदी की current (या पानी का flow) किसी नाव की effective speed को कैसे प्रभावित करती है। बहाव (current) की दिशा motion को सहायक या विरोधी बना देती है।

यह pattern important है क्योंकि कई aptitude सवालों में upstream (current के खिलाफ) और downstream (current के साथ) motion आते हैं - और इस concept को समझ लेने से distance-speed वाले जटिल सम्बंध भी आसानी से handle हो जाते हैं।

Pattern: Boats and Streams (Upstream / Downstream)

Pattern

Key concept: Stream की current या तो नाव के motion को मदद देती है या रोकती है।

  • Downstream (current के साथ): Effective speed = (Boat speed + Stream speed)
  • Upstream (current के खिलाफ): Effective speed = (Boat speed - Stream speed)
  • Still water: जब current = 0 हो तो नाव की speed उसकी own speed होती है।
  • Average relation:
    • Speed in still water = (Downstream + Upstream) ÷ 2
    • Speed of current = (Downstream - Upstream) ÷ 2

Step-by-Step Example

Question

एक नाव 24 km downstream में 3 hours में जाती है और वही दूरी वापसी में upstream 4 hours लेती है। नाव की still water में speed और stream की speed क्या है?

Solution

  1. Step 1: Downstream और Upstream speeds निकालें

    Downstream speed = 24 ÷ 3 = 8 km/h
    Upstream speed = 24 ÷ 4 = 6 km/h

  2. Step 2: Still water और current के लिए formula लगाएँ

    Speed in still water = (8 + 6) ÷ 2 = 7 km/h
    Speed of stream = (8 - 6) ÷ 2 = 1 km/h

  3. Final Answer:

    नाव की speed in still water = 7 km/h, Current की speed = 1 km/h

  4. Quick Check:

    Downstream = 7 + 1 = 8 km/h, Upstream = 7 - 1 = 6 km/h ✅

Quick Variations

1. Still water में नाव की speed या stream की speed निकालना जब downstream और upstream दी हों।

2. दोनों तरफ यात्रा करते समय time या distance निकालना।

3. जब कोई व्यक्ति या वस्तु moving water पर चले तो relative speed का उपयोग।

4. Current की speed को नाव की speed का fraction (जैसे one-third या one-fifth) दिया गया हो।

5. Units conversion वाले सवाल (जैसे m/s ↔ km/h)।

Trick to Always Use

  • Step 1: Downstream और Upstream के formulas स्पष्ट लिखें।
  • Step 2: (D + U)/2 से नाव की speed और (D - U)/2 से stream की speed निकालें।
  • Step 3: Units हमेशा consistent रखें (कहां km/h और कब m/s)।
  • Step 4: उत्तर की सत्यता के लिए reverse calculation करके verify करें (add/subtract करके D और U वापस पाएँ)।

Summary

Summary

  • Downstream = Boat + Stream
  • Upstream = Boat - Stream
  • Boat speed = (Downstream + Upstream) ÷ 2
  • Stream speed = (Downstream - Upstream) ÷ 2
  • ज़रूरी होने पर units convert करें और accuracy के लिए cross-verification करें।

Practice

(1/5)
1. A boat goes 16 km downstream in 2 hours and returns the same distance upstream in 4 hours. Find the speed of the boat in still water.
easy
A. 6 km/h
B. 7 km/h
C. 8 km/h
D. 9 km/h

Solution

  1. Step 1: Compute downstream & upstream speeds

    Downstream = 16 ÷ 2 = 8 km/h; Upstream = 16 ÷ 4 = 4 km/h.

  2. Step 2: Use formula for still water

    Boat speed = (Downstream + Upstream) ÷ 2 = (8 + 4) ÷ 2 = 6 km/h.

  3. Final Answer:

    Boat speed in still water = 6 km/h → Option A.

  4. Quick Check:

    Downstream = 6 + 2 = 8; Upstream = 6 - 2 = 4 ✅
Hint: Boat = (Down + Up)/2; Stream = (Down - Up)/2.
Common Mistakes: Confusing downstream/upstream speeds or averaging the two speeds incorrectly.
2. A man rows downstream at 10 km/h and upstream at 6 km/h. Find his speed in still water.
easy
A. 7 km/h
B. 8 km/h
C. 9 km/h
D. 10 km/h

Solution

  1. Step 1: Identify downstream & upstream speeds

    Downstream = 10 km/h; Upstream = 6 km/h.

  2. Step 2: Compute still water speed

    Boat speed = (10 + 6) ÷ 2 = 8 km/h.

  3. Final Answer:

    Speed in still water = 8 km/h → Option B.

  4. Quick Check:

    Stream = (10 - 6) ÷ 2 = 2; 8 + 2 = 10, 8 - 2 = 6 ✅
Hint: Add and half for boat speed; subtract and half for stream speed.
Common Mistakes: Taking the simple average without considering downstream/upstream relation.
3. The speed of a boat in still water is 9 km/h, and the stream speed is 2 km/h. Find the time to go 22 km downstream.
easy
A. 2 h
B. 2.2 h
C. 2.4 h
D. 2.5 h

Solution

  1. Step 1: Compute downstream speed

    Downstream = Boat + Stream = 9 + 2 = 11 km/h.

  2. Step 2: Time = Distance ÷ Speed

    Time = 22 ÷ 11 = 2 hours.

  3. Final Answer:

    Time required = 2 hours → Option A.

  4. Quick Check:

    11 × 2 = 22 km ✅
Hint: Downstream = boat + stream; then use D ÷ S.
Common Mistakes: Using boat speed (9) instead of effective downstream speed (11).
4. A man can row 30 km downstream in 3 hours and the same distance upstream in 5 hours. Find the speed of the stream.
medium
A. 1 km/h
B. 3 km/h
C. 2 km/h
D. 4 km/h

Solution

  1. Step 1: Compute downstream & upstream speeds

    Downstream = 30 ÷ 3 = 10 km/h; Upstream = 30 ÷ 5 = 6 km/h.

  2. Step 2: Stream speed = (Down - Up) ÷ 2

    Stream = (10 - 6) ÷ 2 = 2 km/h.

  3. Final Answer:

    Stream speed = 2 km/h → Option C.

  4. Quick Check:

    Boat speed = (10 + 6) ÷ 2 = 8 km/h; 8 ± 2 → 10 & 6 ✅
Hint: Stream = (D - U) ÷ 2; Boat = (D + U) ÷ 2.
Common Mistakes: Swapping formulas for boat and stream speeds.
5. A boat can travel 18 km downstream in 2 hours and the same distance upstream in 3 hours. Find the boat’s speed in still water and the speed of the stream.
medium
A. 7 & 2 km/h
B. 8 & 1 km/h
C. 9 & 1.5 km/h
D. 7.5 & 1.5 km/h

Solution

  1. Step 1: Compute downstream & upstream speeds

    Downstream = 18 ÷ 2 = 9 km/h; Upstream = 18 ÷ 3 = 6 km/h.

  2. Step 2: Boat & stream speeds

    Boat = (9 + 6) ÷ 2 = 7.5 km/h; Stream = (9 - 6) ÷ 2 = 1.5 km/h.

  3. Final Answer:

    Boat = 7.5 km/h, Stream = 1.5 km/h → Option D.

  4. Quick Check:

    7.5 + 1.5 = 9 (down), 7.5 - 1.5 = 6 (up) ✅
Hint: Boat = (D + U)/2; Stream = (D - U)/2.
Common Mistakes: Averaging the two times instead of using speed formulas.

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