# 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, $$(B_s) = U_s + S_s$$ $$(B_s) = 25 + 7 = 32 \ km/hr$$