Question

5. A, B and C can do a piece of work in 8 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?​

Answer 1

${\large{\red{\pmb{\underline{Given :}}}}}$

• A does his work = 8 days
• B does his work = 12 days
• C does his work = 15 days

${\large{\blue{\pmb{\underline{To Find :}}}}}$

• What will be time taken if they all work together.

${\large{\orange{\pmb{\underline{Solution :}}}}}$

First ,

${\sf{1 \: day \: work \: of \: A = \frac{1}{8} }}$

${\sf{1 \: day \: work \: of \: b= \frac{1}{12} }}$

${\sf{1 \: day \: work \: of \: c = \frac{1}{15} }}$

${\maltese{\sf{Let \: the \: no. \: of \: days \: in \: which \: they \: will \: finish \: work \: be \: x }}}$

Than,

${\bf{A = \frac{1}{8} x}}$

${\bf{B = \frac{1}{12}x }}$

${\bf{C = \frac{1}{15}x }}$

Next,

${\mapsto{\sf{ \frac{1}{8}x + \frac{1}{12} x + \frac{1}{15}x = 1 }}}$

${\purple{\bf{LCM \: of \: 8,12 \: and \: 15 \: is \: 120.}}}$

${\mapsto{\sf{ \frac{15x + 10x + 8x}{120} = 1}}}</u></p><p><u>[tex]{\mapsto{\sf{ \frac{15x + 10x + 8x}{120} = 1}}}$

${\mapsto{\sf{ \frac{33x}{120} = 1}}}$

${\mapsto{\sf{x = {\cancel \frac{120}{33} }}}}$

${\blue{\mapsto{\red{\boxed{\bf{3.63 days}}}}}}$

So,

${\green{\underline{\boxed{\bf{Time = 3.63 days}}}}}$

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