Boat and Stream Aptitude Important Formulas, Definitions, & Examples:


Overview:


Topic Included:Formulas, Definitions & Exmaples.
Main Topic:Quantitative Aptitude.
Quantitative Aptitude Sub-topic:Time Speed and Distance Aptitude Notes & Questions.
Questions for practice:10 Questions & Answers with Solutions.

We are discussing different cases of Boat and Stream here to understand the scenario easily.

Note: If speed of water flow is zero then the speed of boat (\(B_s\)) will be normal.

Case (1): If boat and water moving in the same direction (moving downstream) then speed of boat (\(B_s\)) will be- $$ B_s = D_s - S_s $$

Where,
\(B_s\) = Speed of boat.
\(D_s\) = Speed of downstream.
\(S_s\) = Speed of stream.

Example (1): If a boat goes downstream at the speed of \(10 \ km/hr\), and the speed of stream is \(5 \ km/hr\), then find out the speed of the boat in still water?

Solution: Given values,

Speed of downstream \((D_s) = 10 \ km/hr\),

Speed of stream \((S_s) = 5 \ km/hr\), then speed of boat in still water, $$ (B_s) = D_s - S_s $$ $$ (B_s) = 10 - 5 = 5 \ km/hr $$

Example (2): If a man swim \(60 \ km\) downstream taking \(2 \ hours\), and the speed of stream is \(10 \ km/hr\) then find out the speed of the man in still water?

Solution: Given values,

Speed of downstream \((D_s) = \frac{60}{2} = 30 \ km/hr\),

Speed of stream \((S_s) = 10 \ km/hr\), then speed of man in still water, $$ (B_s) = D_s - S_s $$ $$ (B_s) = 30 - 10 = 20 \ km/hr $$

Case (2): If boat and water moving in the opposite direction (moving upstream) then speed of boat (\(B_s\)) will be- $$ B_s = U_s + S_s $$

Where,
\(B_s\) = Speed of boat.
\(U_s\) = Speed of upstream.
\(S_s\) = Speed of stream.

Example (1): If a boat goes upstream at the speed of \(20 \ km/hr\), and the speed of stream is \(10 \ km/hr\), then find out the speed of the boat in still water?

Solution: Given values,

Speed of upstream \((U_s) = 20 \ km/hr\),

Speed of stream \((S_s) = 10 \ km/hr\), then speed of boat in still water, $$ (B_s) = U_s + S_s $$ $$ (B_s) = 20 + 10 = 30 \ km/hr $$

Example (2): If a boat goes \(100 \ km\) upstream taking \(4 \ hours\) and the speed of stream is \(7 \ km/hr\), then find out the speed of the boat in still water?

Solution: Given values,

Speed of upstream \((U_s) = \frac{100}{4} = 25 \ km/hr\),

Speed of stream \((S_s) = 7 \ km/hr\), then speed of boat in still water, $$ (B_s) = U_s + S_s $$ $$ (B_s) = 25 + 7 = 32 \ km/hr $$