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Agniveer Army CEE Boats & Streams

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This page covers Agniveer Army CEE Boats & Streams with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Boats & Streams— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

Imagine walking on a moving escalator. If you walk in the same direction as the escalator, you move faster. If you walk against it, you move slower. Similarly, water current helps or hinders boat movement

Key Rules

Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2. Speed of current = (Downstream speed - Upstream speed) ÷ 2. Downstream speed = Boat speed + Stream speed. Upstream speed = Boat speed - Stream speed.

Formula BlockMemorise — at least one formula appears in every paper
• Downstream Speed = Speed in still water + Speed of stream
• Upstream Speed = Speed in still water - Speed of stream
• Speed in still water = (Downstream + Upstream) ÷ 2
• Speed of stream = (Downstream - Upstream) ÷ 2
• Time = Distance ÷ Speed
Exam PatternsWhat examiners ask — read before attempting PYQs

Questions typically ask for boat speed in still water, stream speed, time calculations, or distance problems. Common formats include round trips, meeting point problems, and comparative speed questions.

ShortcutsUse these to save 30–60 seconds per question

When distance is same upstream and downstream, use the harmonic mean formula: Average speed = (2 × Downstream speed × Upstream speed) ÷ (Downstream speed + Upstream speed).

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Calculate speeds Downstream speed = 20 ÷ 2 = 10 km/hr Upstream speed = 12 ÷ 3 = 4 km/hr

2
Step 2

Apply formulas Boat speed in still water = (10 + 4) ÷ 2 = 7 km/hr Stream speed = (10 - 4) ÷ 2 = 3 km/hr Worked Example 2: A man can row 6 km/hr in still water. Stream speed is 2 km/hr. How long to travel 16 km downstream and return?

1
Step 1

Calculate effective speeds Downstream speed = 6 + 2 = 8 km/hr Upstream speed = 6 - 2 = 4 km/hr

2
Step 2

Calculate times Time downstream = 16 ÷ 8 = 2 hours Time upstream = 16 ÷ 4 = 4 hours Total time = 2 + 4 = 6 hours Trick for Round Trips: Total time = Distance × 2 × Boat speed ÷ (Boat speed² - Stream speed²)

Exam TrapsCommon mistakes students make — avoid these

Students often confuse downstream and upstream directions. Remember: downstream means 'with the flow' (faster), upstream means 'against the flow' (slower). Another trap is adding stream speed when calculating upstream speed instead of subtracting it.

Always check if your downstream speed is greater than upstream speed.

Key Points to Remember

  • Downstream speed = Boat speed + Stream speed (water helps movement)
  • Upstream speed = Boat speed - Stream speed (water opposes movement)
  • Boat speed in still water = (Downstream + Upstream speeds) ÷ 2
  • Stream speed = (Downstream - Upstream speeds) ÷ 2
  • Downstream speed is always greater than upstream speed
  • For same distance upstream and downstream, use harmonic mean for average speed
  • Round trip time = 2D × Boat speed ÷ (Boat speed² - Stream speed²)
  • If stream speed equals boat speed, upstream movement becomes impossible
  • Time upstream is always more than time downstream for same distance
  • When stream speed is zero, upstream speed equals downstream speed

Exam-Specific Tips

  • Downstream speed formula: Speed in still water + Stream speed
  • Upstream speed formula: Speed in still water - Stream speed
  • Speed in still water = (Downstream + Upstream) ÷ 2
  • Stream speed = (Downstream - Upstream) ÷ 2
  • Round trip average speed = (2 × Downstream × Upstream) ÷ (Downstream + Upstream)
  • If boat speed < stream speed, upstream movement is impossible
  • Time ratio upstream:downstream = Downstream speed:Upstream speed
  • For equal time upstream and downstream, distances are in ratio of speeds
Practice MCQs

Boats & Streams — Practice Questions

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A boat travels 60 km downstream in 3 hours. If the speed of the current is 4 km/h, what is the speed of the boat in still water?

Practice 2easy

A man can row upstream at 8 km/h and downstream at 12 km/h. What is the speed of the current?

Practice 3easy

A boat's speed in still water is 15 km/h and the current flows at 3 km/h. How long will it take the boat to cover 108 km upstream?

Practice 4medium

A boat travels 24 km downstream in 2 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Practice 5medium

A man can row upstream at 6 km/h and downstream at 14 km/h. What is the speed of the stream?

Practice 6medium

A boat's speed in still water is 9 km/h and the stream's speed is 3 km/h. How long will it take the boat to travel 48 km upstream?

Practice 7medium

A boat covers 30 km downstream in 3 hours and 30 km upstream in 6 hours. What is the speed of the boat in still water?

Practice 8hard

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. What is the speed of the boat in still water?

60-Second Revision — Boats & Streams

  • Remember: Downstream = Boat + Stream, Upstream = Boat - Stream
  • Formula: Still water speed = (Down + Up) ÷ 2, Stream = (Down - Up) ÷ 2
  • Trap: Never add stream speed to upstream calculation
  • Quick check: Downstream speed > Upstream speed always
  • Round trips: Use harmonic mean for average speed calculation
  • Time relationship: More time upstream than downstream for same distance
  • Direction clarity: With current = Downstream, Against current = Upstream
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