Question

A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. If A, B, C works together, in how many days will they finish the work​

Answer 1

$\bf\purple{\underline{\boxed{Question}}}$

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A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. If A, B, C works together, in how many days will they finish the work

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$\bf\purple{\underline{\boxed{Solution}}}$

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$\small\tt{Time\:taken\:by \:(A+B)\: to\: finish\: the\: work\:}\\{\small\tt{ =\: 18 \:days.}}$

$\small\tt{(A + B)\: 1\: day's\: work\: =\: {\frac{1}{18}}}$

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$\small\tt{Time\:taken\:by \:(B+C)\: to\: finish\: the\: work\:}\\{\small\tt{ =\: 24 \:days.}}$

$\small\tt{(B+ C)\: 1\: day's\: work\: =\: {\frac{1}{24}}}$

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$\small\tt{Time\:taken\:by \:(C+A)\: to\: finish\: the\: work\:}\\{\small\tt{ =\: 36\:days.}}$

$\small\tt{(C+ A)\: 1\: day's\: work\: =\: {\frac{1}{36}}}$

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$\small\tt{Therefore\:,\: 2(A + B + C)'s\: 1\: day's\: work\:}$

$\small\tt{\:=\:{\frac{1}{18}}+{\frac{1}{24}}+{\frac{1}{36}}}$

$\small\bf{\:=\frac{4+3+2}{72}}$

$\small\bf{\:=\:{\cancel\frac{9}{72}}\:=\: {\frac{1}{8}}}$

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$\small\tt\red{(A + B + C)'s\:1 \:day's \:work\:=\:{\frac{1}{2}}\times{\frac{1}{8}}\: =\:{\frac{1}{16}}}$

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$\bf\purple{\underline{\boxed{Thanks}}}$

Answer 2

$\bf\green{\underline{\boxed{Answer}}}$ ✔️

$<font color=red>$☞︎︎︎ Time taken by,

$<font color=black>$ (A+B) to finish the work = 18 days

(A + B) 1 day's work = 1 / 18

$<font color=</strong><strong>blue</strong><strong>>$☞︎︎︎ Time taken by,

$<font color=black>$(B+C) to finish the work = 24 days

(B+ C) 1 day's work = 1 / 24

$<font color=</strong><strong>orange</strong><strong>>$☞︎︎︎ Time taken by,

$<font color=black>$(C+A) to finish the work = 36 days.

(C+ A) 1 day's work = 1 / 36

$<font color=black>$━━━━━━━━━━━━━━━━━━━━━━━━━

$<font color=</strong><strong> </strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>>$☟︎︎︎ Therefore,

$<font color=</strong><strong>black</strong><strong>>$2(A + B + C)'s 1 day's work

= 1/18 + 1/24 + 1/36

= 4+3+2 / 72

= 9/72

= 1/8

$<font color=</strong><strong>green</strong><strong>>$☞︎︎︎ (A + B + C)'s 1 day's work

$<font color=black>$= 1/2 × 1/8

= 1 / 16 .........✪

$<font color=red>$━━━━━━━━✧༺❤༻✧━━━━━━━━

$<p style="color:red;font-family:cursive;background:white;font-size:30px;">Thank you mate✍︎</p>$ ❣️