Question

A and B can do a piece of work in 6 days and 4 days respectively. A started the work; worked at it for 2 days and then was joined by B. Find the total time taken to complete the work

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• A and B can do a piece of work in 6 days and 4 days respectively

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• A started the work 2 days earlier than B

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Total time taken to complete the work

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the total time taken to complete the work be "x"

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$\underline{\bold{\texttt{A's one day work :}}}$

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➠ $\sf \dfrac { 1 } { 6 }$

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$\underline{\bold{\texttt{B's one day work :}}}$

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➠ $\sf \dfrac { 1 } { 4 }$

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As "A" started the work alone from the first day thus "A" will work for "x" days to complete the work.

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As "B" started the work 2 days after "A" thus "B" will work for "x - 2" days to complete the work.

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$\underline{\bold{\texttt{A's work in x days :}}}$

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➠ $\sf x \times \dfrac { 1 } { 6 }$

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$\underline{\bold{\texttt{B's work in (x - 2) days :}}}$

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➠ $\sf (x - 2) \times \dfrac { 1 } { 4 }$

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As we assumed that they will complete the work in x days while counting from the very first day.

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So,

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➜ $\sf x \times \dfrac { 1 } { 6 } + (x - 2) \times \dfrac { 1 } { 4 } = 1$

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➜ $\sf \dfrac { x } { 6 } + \dfrac { x - 2 } { 4 } = 1$

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➜ $\sf \dfrac { 2x + 3x - 6 } { 12 } = 1$

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➜ $\sf \dfrac { 5x - 6 } { 12 } = 1$

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➜ 5x - 6 = 12

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➜ 5x = 12 + 6

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➜ 5x = 18

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➨ x = 3.6 days

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• Hence A & B together can finish the work in 3.6 days

Answer 2

Answer:

X=3.6 days this is answered