Question

A and B together can do a piece of work in 36 days, B and C together can do it in 24 days. A and C together can do it in 18 days. The three working together can finish the work in

A) 8 days B) 16 days C) 30 days D) 32 days

Answer 1

Answer:

A+B=36. 1/A+1/B=1/36

B+C=24. 1/B+1/C=1/24

A+C=18. 1/A+1/C=1/18

2(A+B+C)=1/36+1/24+1/18. Now here is the main method now u can solve

Answer 2

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

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$\green{\underline \bold{Given :}}$

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• A and B together can do a piece of work in 36 days

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• B and C together can do it in 24 days

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• A and C together can do it in 18 days

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$\red{\underline \bold{To \: Find:}}$

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• Days required when the three are working together

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

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Working together, in one day A and B

complete

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$\sf \longmapsto (A + B)s \: 1 \: day \: work \: = \dfrac { 1 } { 36 }$ -----(1)

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Working together, in one day B and C

complete

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$\sf \longmapsto (B + C)s \: 1 \: day \: work \: = \dfrac { 1 } { 24 }$ ------(2)

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Working together, in one day A and C

complete

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$\sf \longmapsto (A + C)s \: 1 \: day \: work \: = \dfrac { 1 } { 18 }$ ------(3)

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$\underline{\bold{\texttt{Adding (1) , (2) \& (3)}}}$

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$\sf \longmapsto 2(A + B + C)s \: 1 \: day \: work \: = \dfrac { 1 } { 36 } + \dfrac { 1 } { 24 } + \dfrac { 1 } { 18 }$

$\:\:$

$\sf \longmapsto 2(A + B + C)s \: 1 \: day \: work \: = \dfrac { 4 + 3 + 2 } { 72 }$

$\:\:$

$\sf \longmapsto 2(A + B + C)s \: 1 \: day \: work \: = \dfrac { 1 } { 8 }$

$\:\:$

$\sf \longmapsto (A + B + C)s \: 1 \: day \: work \: = \dfrac { 1 } { 8 }\times2$

$\:\:$

$\sf \longmapsto (A + B + C)s \: 1 \: day \: work \: = \dfrac { 1 } { 16 }$

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Hence A , B , C working together can finish the work in 16 days

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$\red{\bold{Hence \: , \: Option \: B) \: is \: correct}}$

$\rule{200}5$