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(D) Let $B$ take $x$ days to finish the work.Then,$A$ takes $2x$ days and $C$ takes $3x$ days to complete the same work.The work done by $A, B,$ and $

Vedclass · Accepted Answer

$44$

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(D) Let $B$ take $x$ days to finish the work.Then,$A$ takes $2x$ days and $C$ takes $3x$ days to complete the same work.The work done by $A, B,$ and $C$ in one day is $\frac{1}{2x}, \frac{1}{x},$ and $\frac{1}{3x}$ respectively.Given that working together they finish the work in $12$ days,their combined one-day work is $\frac{1}{12}$.Therefore,$\frac{1}{2x} + \frac{1}{x} + \frac{1}{3x} = \frac{1}{12}$.Finding a common denominator $(6x)$: $\frac{3 + 6 + 2}{6x} = \frac{1}{12}$.$\frac{11}{6x} = \frac{1}{12}$.Cross-multiplying: $6x = 11 	imes 12 = 132$.$x = \frac{132}{6} = 22$ days.Since $A$ takes $2x$ days,the time taken by $A$ alone is $2 	imes 22 = 44$ days.

$A$ takes twice as much time as $B$ and $C$ takes thrice as much time as $B$ to finish a piece of work. Working together they can finish the work in $12$ days. The number of days needed for $A$ to do the work alone is:

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