A can do a pieces of work in $14 d a y s$ while $B$ can do it in $21 d a y s$ . They began together and worked for $7 d a y s$ . Then, A fell ill and $B$ has to complete the work. In how many days was the work completed?

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Solution

Let work be $W .$
$\Rightarrow$ Work done by A in $1$ day $= \frac{W}{14}$

Work done by B in $1$ day $= \frac{W}{21}$
Both work for days $= 7 W (\frac{1}{14} + \frac{1}{21}) = \frac{5 W}{6}$
Let B work alone for $x$ more days to complete,
$\Rightarrow \frac{W x}{21} + \frac{5 W}{6} = W$
$\Rightarrow \frac{x}{21} + \frac{5}{6} = 1$
$\Rightarrow x = \frac{21}{6}$
$= 3.5$
$= 3$ and a half days.
Hence, the answer is $3$ and a half days.

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A can do a pieces of work in 14 days while B can do it in 21 days. They began together and worked for 7 days. Then, A fell ill and B has to complete the work. In how many days was the work completed?

Let work be W.⇒ Work done by A in 1 day =W14 Work done by B in 1 day =W21Both work for days =7W(114+121)=5W6Let B work alone for x more days to complete,⇒Wx21+5W6=W⇒x21+56=1⇒x=216 =3.5 =3 and a half days.Hence, the answer is 3 and a half days.

A can do a pieces of work in $14 d a y s$ while $B$ can do it in $21 d a y s$ . They began together and worked for $7 d a y s$ . Then, A fell ill and $B$ has to complete the work. In how many days was the work completed?