Important Formulas on Streams

Streams - Important Aptitude formulas, shortcut methods and tricks:

Theorem: (1). If α 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.

Theorem: (2). 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
              ɣ (α² - β²)/2α

Theorem: (3). 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
             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.

Streams Aptitude:
Formula:                Streams Aptitude Formulas
Solved Examples:  Solved Examples: Set 01
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