Question

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

• A. $4$ days
• B. $5$ days
• C. $9$ days
• D. $10$ days

Answer 1

Answer: (D)

$10$ days

Percentage Method:

A can complete work in $9$ days

So, percentage of work A completes in one day $=\frac{100}{9}=11.11\%$

B can complete the work in 12 days

B's one day work $=\frac{100}{12}=8.33\%$

A and B together can complete $=11.11+8.33=19.44\%$ of work in one day.

Now,

Take 2 days $=1$ unit of time (one day of A and one day of B)

In one unit of time A and B can complete work $=19.44\%$ work.

Total time unit they need to complete whole work $=\frac{100}{19.44}=5$ time unit approx.

Thus, Total time $=5$ time unit $=5\times 2=10$ days.

Fraction Method:

A can complete total work 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,

$=\frac{1}{9}+\frac{1}{12}$

$=\frac{4+3}{36}=\frac{7}{36}$ part

Take, $2$ days $=1$ time unit

To time unit needed to complete the work,

$=\frac{1}{\frac{7}{36}}=\frac{36}{7}=5$ time unit approx.

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