A man, a boy and a woman can finish a work in 10 days, 15 days and 30 days, respectively. In how many days can the work be finished by a man, a woman and a boy when all of them work together?

The correct answer is 5 days.

We are given that:

- A man can finish the work alone in 10 days
- A boy can finish the work alone in 15 days
- A woman can finish the work alone in 30 days

Step 1: Find the one-day work (efficiency) of each person.

The fraction of work done in one day is the reciprocal of the number of days taken.

One day's work of the man = \frac{1}{10}

One day's work of the boy = \frac{1}{15}

One day's work of the woman = \frac{1}{30}

Step 2: Find the combined one-day work of all three working together.

Combined work per day = \frac{1}{10}+\frac{1}{15}+\frac{1}{30}

To add these fractions, we find the LCM of 10, 15, and 30, which is 30.

\frac{1}{10}+\frac{1}{15}+\frac{1}{30}=\frac{3}{30}+\frac{2}{30}+\frac{1}{30}=\frac{3+2+1}{30}=\frac{6}{30}=\frac{1}{5}

Step 3: Find the total number of days to complete the work.

If all three together complete \frac{1}{5} of the work in one day, then the total number of days required to finish the entire work is the reciprocal:

Total days = \frac{1}{\frac{1}{5}}=5 days

Therefore, the man, woman, and boy together can finish the work in 5 days.