P and Q can do a piece of work in 30 and 40 d | vedclass

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(C) Work done by $Q$ alone in $12$ days $= \frac{12}{40} = \frac{3}{10}$ of the total work.Remaining work to be done by $P$ and $Q$ together $= 1 - \f

Vedclass · Accepted Answer

$12$

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(C) Work done by $Q$ alone in $12$ days $= \frac{12}{40} = \frac{3}{10}$ of the total work.Remaining work to be done by $P$ and $Q$ together $= 1 - \frac{3}{10} = \frac{7}{10}$ of the total work.$P$'s one day work $= \frac{1}{30}$ and $Q$'s one day work $= \frac{1}{40}$.Combined one day work of $P$ and $Q = \frac{1}{30} + \frac{1}{40} = \frac{4+3}{120} = \frac{7}{120}$.Time taken by $P$ and $Q$ to complete $\frac{7}{10}$ of the work $= \frac{7/10}{7/120} = \frac{7}{10} 	imes \frac{120}{7} = 12$ days.Therefore,$P$ left after $12$ days.

$P$ and $Q$ can do a piece of work in $30$ and $40$ days respectively. They began the work together,but $P$ left after some days and $Q$ finished the remaining work in $12$ days. After how many days did $P$ leave?

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