A, B, and C can do a work separately in 16, 3 | vedclass

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(B) Let the total time taken to complete the work be $x$ days.Since $A$ worked for the entire duration,$B$ left $8$ days before completion,and $C$ lef

Vedclass · Accepted Answer

$12$

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(B) Let the total time taken to complete the work be $x$ days.Since $A$ worked for the entire duration,$B$ left $8$ days before completion,and $C$ left $6$ days before completion,their individual work contributions are:Work done by $A = \frac{x}{16}$Work done by $B = \frac{x-8}{32}$Work done by $C = \frac{x-6}{48}$The sum of their work equals $1$ (the whole work):$\frac{x}{16} + \frac{x-8}{32} + \frac{x-6}{48} = 1$Taking the least common multiple $(LCM)$ of $16, 32,$ and $48$,which is $96$:$\frac{6x + 3(x-8) + 2(x-6)}{96} = 1$$6x + 3x - 24 + 2x - 12 = 96$$11x - 36 = 96$$11x = 132$$x = \frac{132}{11} = 12$ days.Thus,the work is finished in $12$ days.

$A,$ $B,$ and $C$ can do a work separately in $16,$ $32,$ and $48$ days respectively. They started the work together,but $B$ left $8$ days before and $C$ left $6$ days before the completion of the work. In what time is the work finished? (in days)

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