A and B together can complete a work in 8 day | vedclass

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(C) Time taken by $B$ to complete the work $= 12$ days.Time taken by $A$ and $B$ together to complete the work $= 8$ days.Efficiency of $A$ and $B$ to

Vedclass · Accepted Answer

$16$

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(C) Time taken by $B$ to complete the work $= 12$ days.Time taken by $A$ and $B$ together to complete the work $= 8$ days.Efficiency of $A$ and $B$ together $= \frac{1}{8}$ work/day.Efficiency of $B$ alone $= \frac{1}{12}$ work/day.Efficiency of $A$ alone $= \frac{1}{8} - \frac{1}{12} = \frac{3-2}{24} = \frac{1}{24}$ work/day.Thus,$A$ alone can complete the work in $24$ days.Work done by $B$ in $4$ days $= 4 	imes \frac{1}{12} = \frac{1}{3}$.Remaining work $= 1 - \frac{1}{3} = \frac{2}{3}$.Time taken by $A$ to complete the remaining work $= \frac{	ext{Remaining work}}{	ext{Efficiency of } A} = \frac{2/3}{1/24} = \frac{2}{3} 	imes 24 = 16$ days.

$A$ and $B$ together can complete a work in $8$ days. $B$ alone can complete that work in $12$ days. $B$ alone worked for $4$ days. After that,how long will $A$ alone take to complete the remaining work?

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