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1. A and B together can do a piece of work in 8 days, B and C together in 10 days, while C and A together in 6 days, if they all work together the work will be completed in ?

A. $3 \frac{3}{4} days$

B. $3 \frac{3}{7} days$

C. $5 \frac{5}{47} days$

D. $4 \frac{4}{9} days$

Solution:

In these kind of questions, always take total work as L.C.M. of number of days
Here L.C.M. of Total Work = 120
One day work of A + B =

\frac{120}{8}

= 15 unit/day
One day work of B + C =

\frac{120}{10}

= 12 unit/day
One day work of C + A =

\frac{120}{6}

= 20 unit/day
∴ Total units per day = 15 + 12 + 20 = 47
∴ Efficiency of :

\begin{aligned} 2 (A + B + C) = 47 \\ A + B + C = \frac{47}{2} \end{aligned}

(A + B + C) will complete the whole work in

\begin{aligned} = \frac{120}{\frac{47}{2}} \\ = \frac{240}{47} \\ = 5 \frac{5}{47} days \end{aligned}

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