Question

a can do a piece of work in 6 days and B can do it in 9 days how long will they take to complete the same work together​

Answer 1

Step-by-step explanation:

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Answer 2

AnswEr :

$\underline{\large{\bf{\dag}\:\textit{Method 1:}}}$

$\frak{Given}\begin{cases}\texttt{A can do work in = 6 Days}\\\texttt{B can do work in = 9 Days}\\\texttt{(A + B)'s will do work in = ?}\end{cases}$

$\underline{\bigstar\:\textsf{Let's Head to the Question Now :}}$

$:\implies\tt (A + B)'s \:will \:take = \dfrac{A \times B}{A+B}\\\\\\:\implies\tt (A + B)'s \:will\:take = \dfrac{6 \times 9}{6+9}\\\\\\:\implies\tt (A + B)'s \:will \:take =\dfrac{54}{15}\\\\\\:\implies\underline{\boxed{\tt (A + B)'s\:will\:take = 3.6 \:Days}}$

⠀

$\therefore\:\underline{\textsf{A \& B will together complete work in \textbf{3.6 Days}}}$

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$\underline{\large{\bf{\dag}\:\textit{Method 2:}}}$

Let the Time Taken to Complete work together by A and B be x days.

$\dashrightarrow\:\:\tt \dfrac{Time}{A's\:Rate}+\dfrac{Time}{B's\:Rate}=Total\:Work\\\\\\\dashrightarrow\:\:\tt \dfrac{x}{6} +\dfrac{x}{9} = 1\\\\\\\dashrightarrow\:\:\tt\dfrac{3x + 2x}{18} = 1\\\\\\\dashrightarrow\:\:\tt\dfrac{5x}{18} = 1\\\\\\\dashrightarrow\:\:\tt x =\dfrac{18}{5}\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt x = 3.6 \:Days}}$

⠀

$\therefore\:\underline{\textsf{A \& B will together complete work in \textbf{3.6 Days}}}$