Cheatsheet: Boat & Stream | IBPS PO Prelims & Mains Preparation - Bank Exams PDF Download

Introduction

Boat and Stream problems are a common part of quantitative aptitude tests, assessing your ability to calculate speeds and travel times when a boat moves in flowing water (stream). These problems involve understanding how the speed of the boat changes based on the direction of the stream (with or against the flow).

Key Concepts & Theory

1. Still Water – Speed of the boat in calm water (no current).

2. Stream Speed – Speed of the water current (can be aiding or opposing the boat).

3. Downstream – Boat moves with the stream (speeds add up).

4. Upstream – Boat moves against the stream (speeds subtract).

Formulas

1. Basic Speed Formulas

• Downstream Speed (D.S.) = Boat Speed (B) + Stream Speed (S)

• Upstream Speed (U.S.) = Boat Speed (B) – Stream Speed (S)

2. Finding Boat & Stream Speed

• Boat Speed (B) = (D.S. + U.S.) / 2

• Stream Speed (S) = (D.S. – U.S.) / 2

3. Time, Distance, and Speed Relations

• Time = Distance / Speed

• Distance = Speed × Time

4. Special Cases

• If downstream speed is x times upstream speed:

  • Boat Speed (B) = S × (x + 1) / (x – 1)

  • Stream Speed (S) = B × (x – 1) / (x + 1)

Tips & Tricks

1. Always Define Variables Clearly

• Let B = Boat speed in still water

• Let S = Stream speed

2. Use Ratios for Faster Calculations

• If downstream speed = 15 km/h and upstream speed = 5 km/h:

  • Boat Speed (B) = (15 + 5)/2 = 10 km/h

  • Stream Speed (S) = (15 – 5)/2 = 5 km/h

3. Shortcut for Equal Distances

• If a boat travels the same distance upstream and downstream:

  • Average Speed = (2 × D.S. × U.S.) / (D.S. + U.S.)

4. Relative Speed Concept

• Two boats moving in the same/opposite directions:

  • Same Direction: Subtract speeds

  • Opposite Direction: Add speeds

5. Approximation for Exams

• If exact calculation is complex, estimate using nearest whole numbers.

Example Problems

Example 1: Basic Speed Calculation

• A boat goes 12 km/h downstream and 8 km/h upstream. Find boat and stream speeds.

  • Boat Speed (B) = (12 + 8)/2 = 10 km/h

  • Stream Speed (S) = (12 – 8)/2 = 2 km/h

Example 2: Time Calculation

• A boat travels 30 km downstream in 2 hours and 20 km upstream in 5 hours. Find speeds.

  • D.S. = 30/2 = 15 km/h

  • U.S. = 20/5 = 4 km/h

  • B = (15 + 4)/2 = 9.5 km/h

  • S = (15 – 4)/2 = 5.5 km/h

Final Exam Tips

• Memorize the basic formulas (D.S. = B + S, U.S. = B – S).
• Practice problems with different variations (time-based, distance-based).
• Check units and direction (upstream/downstream) carefully.
• Use elimination in MCQs if exact calculation takes time.

Conclusion

Boat and Stream problems are easy once you understand the direction of movement and speed relations. With consistent practice, you can solve these questions quickly and accurately in exams.

Happy Learning !