If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man , 1 woman and 1 boy in

Options

A. 21 days
B. 24 days
C. 26 days
D. 33 days

Answer

To solve the problem, we need to determine how long it will take for 1 man, 1 woman, and 1 boy to complete a piece of work together, given that 1 man or 2 women or 3 boys can complete the work in 44 days.

### Step-by-Step Solution:

1. **Determine the work done by each individual:**
- Let the total work be represented as 1 unit.
- If 1 man can complete the work in 44 days, then the work done by 1 man in 1 day is:
\[ \text{Work done by 1 man in 1 day} = \frac{1}{44} \]

- If 2 women can complete the work in 44 days, then the work done by 1 woman in 1 day is:
\[ \text{Work done by 1 woman in 1 day} = \frac{1}{2 \times 44} = \frac{1}{88} \]

- If 3 boys can complete the work in 44 days, then the work done by 1 boy in 1 day is:
\[ \text{Work done by 1 boy in 1 day} = \frac{1}{3 \times 44} = \frac{1}{132} \]

2. **Calculate the combined work done by 1 man, 1 woman, and 1 boy in 1 day:**
- The total work done by 1 man, 1 woman, and 1 boy in 1 day is:
\[ \text{Total work in 1 day} = \frac{1}{44} + \frac{1}{88} + \frac{1}{132} \]

3. **Find a common denominator to add the fractions:**
- The least common multiple (LCM) of 44, 88, and 132 is 264.
- Convert each fraction:
\[ \frac{1}{44} = \frac{6}{264}, \quad \frac{1}{88} = \frac{3}{264}, \quad \frac{1}{132} = \frac{2}{264} \]
- Now, add them:
\[ \text{Total work in 1 day} = \frac{6}{264} + \frac{3}{264} + \frac{2}{264} = \frac{11}{264} \]

4. **Determine how many days it will take to complete the work:**
- If they can do \(\frac{11}{264}\) of the work in 1 day, the total time \(X\) to complete 1 unit of work is:
\[ X = \frac{1}{\frac{11}{264}} = \frac{264}{11} = 24 \text{ days} \]

### Final Answer:
Thus, 1 man, 1 woman, and 1 boy together can complete the work in **24 days**.

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