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: Next Tests