Question

A man
can row upstream 10kmph
and downstream 20kmph. Find the
man rate in still water and rate
of the
stream.​

Answer 1

$\maltese\LARGE\textsf{\underline{ SoLuTioN :-}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Let the speed of the boat in still water be " x "}$

$\qquad\tt{:}\longrightarrow\large\textsf{Let the speed of the stream be " y "}$

$\large\textsf{ }$

↦ Speed of the boat upstream

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{purple}{x - y = 10 -----( i )}}$

$\large\textsf{ }$

↦ Speed of the boat downstream

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{purple}{x + y = 20 -----( ii )}}$

$\large\textsf{ }$

↦ Add ( i ) & ( ii )

$\large\textsf{ }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf\: x \: \: \: - \: \: \: \cancel y \: \: \: = \: \: \: 10 \\( \: + \: ) \: \: \: \: \: \: \sf \: x \: \: \: + \: \: \: \cancel y \: \: \: = \: \: \: 20 \\ - - - - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: 2x \: \: = \: \: 30 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x \: \: \: = \: \: \: \xcancel\cfrac{30}{2} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore \boxed{ \sf \color{red} x \: \: \: = \: \: \: 15}$

$\large\textsf{ }$

↦ Substitute the value of " x " in ( ii )

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{15 + y = 20}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{y = 20 - 15}\\\\\\\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{y = 5}}$

$\large\textsf{ }$

$\boxed{\begin{array}{c}\leadsto\large\textsf\textcolor{orange}{Speed of the boat in still water = 15 km \ hr}\\\\\leadsto\large\textsf\textcolor{orange}{Speed of the stream = 5 km \ hr }\end{array}}$

Answer 2

Answer:

answer is 15 and 5

Step-by-step explanation:

Please remember,

If a is rate downstream and b is rate upstream

Rate in still water = 1/2(a+b)

Rate of current = 1/2(a-b)

=> Rate in still water = 1/2(20+10) = 15 kmph

=> Rate of current = 1/2(20-10) = 5 kmph