| 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.
Case (3): If speed of downstream \((D_s)\) and speed of upstream \((U_s)\) are given in the question then speed of boat in still water,$$ \left[B_s = \frac{D_s + U_s}{2}\right] $$ and speed of stream, $$ \left[S_s = \frac{D_s - U_s}{2}\right] $$
Where,\(B_s\) = Speed of boat.\(D_s\) = Speed of downstream.\(U_s\) = Speed of upstream.\(S_s\) = Speed of stream.
Example (1): If a boat goes upstream at the speed of \(10 \ km/hr\) and downstream at the speed of \(20 \ km/hr\), then find the speed of boat in still water and also find the speed of stream?
Solution: Given values,Speed of upstream \((U_s) = 10 \ km/hr\),Speed of downstream \((D_s) = 20 \ km/hr\), then $$ \left[Speed \ of \ boat \ (B_s) = \frac{D_s + U_s}{2}\right] $$ $$ \left[Speed \ of \ boat \ (B_s) = \frac{20 + 10}{2}\right] $$ $$ Speed \ of \ boat \ (B_s) = \frac{30}{2} = 15 \ km/hr $$
now,$$ \left[Speed \ of \ stream \ (S_s) = \frac{D_s - U_s}{2}\right] $$ $$ \left[Speed \ of \ stream \ (S_s) = \frac{20 - 10}{2}\right] $$ $$ S_s = \frac{10}{2} = 5 \ km/hr $$
Example (2): If a boat goes upstream at the speed of \(x \ km/hr\) and downstream at the speed of \(15 \ km/hr\), if speed of boat in still water is \(8 \ km/hr\), then find the value of \(x\) and also find the speed of stream?
Solution: Given values,Speed of upstream \((U_s) = x \ km/hr\),Speed of downstream \((D_s) = 15 \ km/hr\), speed of boat in still water \((B_s) = 8 \ km/hr\) then $$ \left[Speed \ of \ boat \ (B_s) = \frac{D_s + U_s}{2}\right] $$ $$ \left[8 = \frac{15 + x}{2}\right] $$ $$ x = U_s = 1 \ km/hr $$
now,$$ \left[Speed \ of \ stream \ (S_s) = \frac{D_s - U_s}{2}\right] $$ $$ \left[Speed \ of \ stream \ (S_s) = \frac{15 - 1}{2}\right] $$ $$ S_s = \frac{14}{2} = 7 \ km/hr $$
Example (3): If a man swim \(25 \ km\) upstream and \(35 \ km\) downstream, taking \(2 \ hours\) each time, then find the speed of the stream?
Solution: Given values,Speed of upstream \((U_s) = \frac{25}{2} = 12.5 \ km/hr\),Speed of downstream \((D_s) = \frac{35}{2} = 17.5 \ km/hr\), then $$ \left[Speed \ of \ stream \ (S_s) = \frac{D_s - U_s}{2}\right] $$ $$ \left[Speed \ of \ stream \ (S_s) = \frac{17.5 - 12.5}{2}\right] $$ $$ S_s = \frac{5}{2} = 2.5 \ km/hr $$