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(D) Efficiency of $A = \frac{1}{24}$ units/day.Efficiency of $B = \frac{1}{30}$ units/day.Efficiency of $C = \frac{1}{40}$ units/day.Total work ($LCM$

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$11$

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(D) Efficiency of $A = \frac{1}{24}$ units/day.Efficiency of $B = \frac{1}{30}$ units/day.Efficiency of $C = \frac{1}{40}$ units/day.Total work ($LCM$ of $24, 30, 40$) $= 120$ units.Efficiency of $A = 5$ units/day,$B = 4$ units/day,$C = 3$ units/day.Combined efficiency of $(A+B+C) = 5+4+3 = 12$ units/day.Let the total time taken to complete the work be $x$ days.$C$ left $4$ days before completion,so $C$ worked for $(x-4)$ days,while $A$ and $B$ worked for $x$ days.Equation: $5x + 4x + 3(x-4) = 120$.$9x + 3x - 12 = 120$.$12x = 132$.$x = 11$ days.Thus,the total work was completed in $11$ days.

$A, B$ and $C$ can do a piece of work in $24, 30$ and $40$ days respectively. They began the work together,but $C$ left $4$ days before the completion of the work. In how many days was the work done?

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