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1. To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take :

A. 7 Days

B. 7.5 Days

C. 8 Days

D. 8.5 Days

Solution:

Given (A+B)'s one day's work =

\frac{1}{8}

(B + C)'s one day's work =

\frac{1}{12}

(A + B + C) 's 1 day's work =

\frac{1}{6}

Work done by A, alone= (A + B + C) 's 1 day's work - (B + C)'s one day's work

= \frac{1}{6} - \frac{1}{12} = \frac{2 - 1}{12} = \frac{1}{12}

Work done by C, alone = (A + B + C) 's 1 day's work - (A + B)'s one day’s work

= \frac{1}{6} - \frac{1}{8} = \frac{4 - 3}{24} = \frac{1}{24}

⇒ (A + C)’s one day’s work

\begin{aligned} = \frac{1}{12} + \frac{1}{24} \\ = \frac{2 + 1}{24} \\ = \frac{3}{24} = \frac{1}{8} \end{aligned}

⇒ (A + C) will take 8 days to complete the work together

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