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__Streams - Important Aptitude formulas, shortcut methods and tricks__:

__Streams - Important Aptitude formulas, shortcut methods and tricks__:

**If α**

__Theorem: (1)__.*km/hr be the man’s rate in still water and β km/hr be the rate of the current, then*

α
+ β = man’s rate with current

α
- β = man’s rate against current

**Note:**(i) A man’s rate in still water is half the sum of his rate with and against the current.

(ii) The rate of the current is half the difference between the rate of
the man with and against the current.

**A man can row α km/hr in still water. If in a stream, which is flowing at β km/hr, it takes him ɣ hrs to row to a place and back. The distance between the two places is**

__Theorem: (2)__.**ɣ (α² - β²)/2α**

**A man rows a certain distance downstream in α hrs and returns the same distance in β hrs. If the stream flows at the rate of ɣ km/hr, then the speed of the man is given by**

__Theorem: (3)__.**ɣ (α + β)/(β - α)**km/hr.

__Example: 01__**A man can row 6 km/hr in still water. It takes him twice as long to row up as to row down the river. Find the rate of the stream.**

__Solution:__
Let, rate of
stream = α km/hr

Then, 6 + α
= 2 (6 - α)

or, α = 2 km/hr.

__Example: 02__**A man can row 6 km/hr in still water. When the water is running at 1.2 km/hr, it takes him 1 hr to row to a place and back. How far is the place?**

__Solution:__
The required
distance = [1 × (6² - 1.2²)]/(2 × 6) = 2.88 km.

__Example: 03__**A man can row 7 km/hr in still water. In a stream which is flowing at 3 km/hr, it takes him 7 hrs to row to a place and back. How far is the place?**

__Solution:__
The required
distance = [7 × (7² - 3²)]/(2 × 7) = 20 km.

__Example: 04__**Jack can row a certain distance downstream in 6 hrs and return to the same distance in 9 hrs. If the stream flows at the rate of 3 km/hr, find the speed of Jack in still water.**

__Solution:__
Jack’s speed
in still water = [3 × (9 + 6)]/(9 - 6) = 15 km/hr.

__Example: 05__**If a man’s rate with the current is 12 km/hr and the rate of the current is 1.5 km/hr. Then what is the man’s rate against the current?**

__Solution:__
Man’s rate
with the current = 12 km/hr

Man’s rate
in still water = 12 - 1.5 = 10.5 km/hr

Therefore, Man’s rate
against current = 10.5 - 1.5 = 9 km/hr.
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