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$A$ can do a piece of work in $14$ days which $B$ can do in $21$ days. They begin together but $3$ days before the completion of the work, $A$ leaves off. The total number of days to complete the work is :

  1. $\frac{33}{5}$
  2. $8\frac{1}{2}$
  3. $\frac{51}{5}$
  4. $13\frac{1}{2}$
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Answer is C

x days (A and B work together) + 3 days (B alone worked) = 1

$x*(\frac{1}{14}+\frac{1}{21})+ 3*\frac{1}{21}=1$

On solving, we will get $5x = 36 \implies x =\frac{36}{5}$

Therefore, total number of days to complete the work = $\frac{36}{5}$ + 3 = $\frac{51}{5}$

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