# Boat and Stream Aptitude Important Formulas:

#### 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.

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 $$\left[Speed \ of \ stream \ (S_s) = \frac{D_s - U_s}{2}\right]$$ $$\left[Speed \ of \ stream \ (S_s) = \frac{17.5 - 12.5}{2}\right]$$ $$S_s = \frac{5}{2} = 2.5 \ km/hr$$