Question : If A, B, and C can do a work in 6 days, 9 days, and 11 days respectively, then, working together, how many days will they take to do the work?
Option 1: $1 \frac{52}{73}$
Option 2: $4 \frac{52}{73}$
Option 3: $2 \frac{52}{73}$
Option 4: $3 \frac{52}{73}$
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Correct Answer: $2 \frac{52}{73}$
Solution :
1 day work of A = $\frac{1}{6}$
1 day work of B = $\frac{1}{9}$
1 day work of C = $\frac{1}{11}$
Together in 1 day they can do = $\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{6}+\frac{1}{9}+\frac{1}{11}$
= $\frac{99+66+54}{594}$
= $\frac{219}{594}$
$\therefore$ A + B + C can do the work in $\frac{594}{219}$ days = $2 \frac{52}{73}$ days
Hence, the correct answer is $2 \frac{52}{73}$.
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