Question

A can do a piece of work in 15 days B does it in 10 days after 3 days B goes away in how many days they will complete the work together​

Answer 1

A n s w e r

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G i v e n

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• A can do a piece of work in 15 days

• B can do the work in 10 days

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F i n d

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After 3 days B goes away in how many days A will complete the work together

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S o l u t i o n

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• Let A can finish the left work in "m" days after B left

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$\underline{\bold{\texttt{One day work of A :}}}$

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A can do a piece of work in 15 days

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➠ $\sf \dfrac { 1 } { 15 }$

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$\underline{\bold{\texttt{One day work of B :}}}$

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B can do the work in 10 days

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➠ $\sf \dfrac { 1 } { 10}$

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$\underline{\bold{\texttt{One day work when A \& B work together :}}}$

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➜ $\sf \dfrac { 1 } { 15 } + \dfrac { 1 } { 10 }$

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➜ $\sf \dfrac { 2 + 3 } { 30 }$

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➜ $\sf \dfrac { 5 } { 30 }$

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➜ $\sf \dfrac { 1 } { 6 }$

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$\underline{\bold{\texttt{3 days work when A \& B work together :}}}$

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➜ $\sf \dfrac { 1 } { 6 } \times 3$

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➜ $\sf \dfrac { 1 } { 2 }$

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$\underline{\bold{\texttt{Remaining work :}}}$

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➜ $\sf 1 - \dfrac { 1 } { 2 }$

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➜ $\sf \dfrac { 2 - 1 } { 2 }$

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➜ $\sf \dfrac { 1 } { 2 }$

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$\underline{\bold{\texttt{"m" days work of A :}}}$

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➜ $\sf \dfrac { 1 } { 15 } \times m$

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As we assumed that A can finish the remaining work in "m" days

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Thus ,

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➜ $\sf \dfrac { 1 } { 15 } \times m = \dfrac { 1 } { 2 }$

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➨ $\sf m = \dfrac { 15 } { 2 }$

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• $\bf Hence \: A \: can \: finish \: the \: remaining \: work \: in \: \dfrac { 15 } { 2 } \: days$

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$\underline{\bold{\texttt{Total days needed to complete work :}}}$

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Number of days both worked together + Number of days A worked alone

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➜ $\sf 3 + \dfrac { 15 } { 2 }$

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➜ $\sf \dfrac { 6 + 15 } { 2 }$

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➨ $\sf \dfrac { 21 } { 2 }$

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$\sf \therefore \: They \: will \: take \: \dfrac { 21 } { 2 } \: days \: to \: complete \: the \: work$