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$A$ and $B$ can complete a task in $30$ days when working together. After $A$ and $B$ have been working together for $11$ days, $B$ is called away and $A$, himself completes the task in the next $28$ days. Had $A$ been working alone, the number of days taken by him to complete the task would have been:

  1. $\dfrac{379}{9} \\$
  2. $\dfrac{840}{19} \\$
  3. $\dfrac{520}{11} \\$
  4. $\dfrac{590}{11}$
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Answer is B

$A+B = \frac{1}{30}$

11 days (A+B) work together + 28 days A alone worked = 1

11*$\frac{1}{30}$ + 28 * A = 1

On solving, we will get A’s 1 day work is $\frac{19}{840}$

No: of days taken by A to complete the work alone is $\frac{840}{19}$

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