If one man or two women or three boys can do a piece of work in 22 days, then the same piece of work will be done by 1 man, 1 boy and 1 women in

Options

A. 8 days
B. 12 days
C. 6 days
D. 11 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the work done by one man, one woman, and one boy in one day.

Given that:
- 1 man can complete the work in 22 days.
- 2 women can complete the work in 22 days.
- 3 boys can complete the work in 22 days.

From this, we can find the work done by each individual in one day.

**Work done by 1 man in one day:**
\[ \text{Work by 1 man in 1 day} = \frac{1}{22} \]

**Work done by 1 woman in one day:**
Since 2 women can do the work in 22 days, the work done by 1 woman in one day is:
\[ \text{Work by 1 woman in 1 day} = \frac{1}{2} \times \frac{1}{22} = \frac{1}{44} \]

**Work done by 1 boy in one day:**
Since 3 boys can do the work in 22 days, the work done by 1 boy in one day is:
\[ \text{Work by 1 boy in 1 day} = \frac{1}{3} \times \frac{1}{22} = \frac{1}{66} \]

### Step 2: Calculate the total work done by 1 man, 1 woman, and 1 boy in one day.

Now, we need to find the total work done by 1 man, 1 woman, and 1 boy in one day:
\[ \text{Total work in 1 day} = \text{Work by 1 man} + \text{Work by 1 woman} + \text{Work by 1 boy} \]
\[ = \frac{1}{22} + \frac{1}{44} + \frac{1}{66} \]

### Step 3: Find a common denominator and add the fractions.

The least common multiple (LCM) of 22, 44, and 66 is 132. Now, we convert each fraction:
\[ \frac{1}{22} = \frac{6}{132}, \quad \frac{1}{44} = \frac{3}{132}, \quad \frac{1}{66} = \frac{2}{132} \]

Now, add them together:
\[ \text{Total work in 1 day} = \frac{6}{132} + \frac{3}{132} + \frac{2}{132} = \frac{11}{132} \]

### Step 4: Calculate the number of days to complete the work.

To find out how many days it will take for 1 man, 1 woman, and 1 boy to complete the work, we take the reciprocal of the total work done in one day:
\[ \text{Days to complete the work} = \frac{1}{\frac{11}{132}} = \frac{132}{11} = 12 \]

### Final Answer:
Thus, 1 man, 1 woman, and 1 boy can complete the work in **12 days**.

---