A and B together can complete a work in 10 da | vedclass

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Question

(C) Let the total work be $10$ units (assuming the rate of $A+B$ is $1$ unit/day).$A+B$ together complete $1$ unit per day.In $2$ days,$A+B$ complete

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(C) Let the total work be $10$ units (assuming the rate of $A+B$ is $1$ unit/day).$A+B$ together complete $1$ unit per day.In $2$ days,$A+B$ complete $2 	imes 1 = 2$ units of work.Remaining work $= 10 - 2 = 8$ units.$B$ completes these $8$ units in $12$ days.Therefore,$B$'s efficiency $= \frac{8}{12} = \frac{2}{3}$ units/day.Since $A+B$ efficiency is $1$ unit/day,$A$'s efficiency $= 1 - \frac{2}{3} = \frac{1}{3}$ units/day.Time taken by $A$ to complete the entire work $= \frac{	ext{Total work}}{	ext{Efficiency of } A} = \frac{10}{1/3} = 30$ days.

$A$ and $B$ together can complete a work in $10$ days. They started together,but $A$ left after $2$ days and the remaining work was completed by $B$ in $12$ days. In how many days can $A$ complete the entire work while working alone?

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