Question

$A$ and $B$ working separately can do a piece of work in $9$ days and $12$ dys respectively, if they work for a alternately, A beginning, in how many days the work will be completed ?

• A. $4$
• B. $5$
• C. $9$
• D. $10$

Answer 1

The correct option is C $9$

$A$ can complete total wok in $9$ days.

One day work of $A$ $=\frac{1}{9}$ part.

$B$ can complete work in $12$ days.

One day work of $B$ $=\frac{1}{12}$ part.

$A$ and $B$ together can complete work in one day $=\frac{1}{9}+\frac{1}{12}=\frac{7}{36}$ part.

Take $2$ days $=1$ time unit

Total time unit needed to complete the work $=\frac{1}{\frac{7}{36}}=\frac{36}{7}=5$ time unit approx.

Therefore, total time $=2\times 5=10$ days.