Question

A can do a piece of work in $20$ days B in $15$ days and C in $12$ days. How soon can the work be done if A is assisted by B on one day and by C on the next alternately?

• A. $14$ days
• B. $6$ days
• C. $8$ days
• D. $10$ days

Answer 1

The correct option is C $8$ days

$(A+B{)}^{\prime }s1day$ work $=(\frac{1}{20}+\frac{1}{15})$ of the work, i.e., $\frac{7}{60}$
$(A+C{)}^{s}1days$ work $=(\frac{1}{20}+\frac{1}{12})$, i.e. $\frac{8}{60}$ of the work.
$2$ days work done $=\frac{7}{60}+\frac{8}{60}=\frac{1}{4}$.
Since $\frac{1}{4}$ of work is done in $2$ days, so whole of the work is done in $8$ days.