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 step by step, we will first determine the work done by each individual (man, woman, and boy) based on the information provided, and then find out how long it will take for one man, one woman, and one boy to complete the work together.

### Step 1: Determine the work done by each individual
According to the problem:
- 1 man can complete the work in 44 days.
- 2 women can complete the work in 44 days.
- 3 boys can complete the work in 44 days.

This means:
- The work done by 1 man in 1 day = 1/44 of the work.
- The work done by 2 women in 1 day = 1/44 of the work, so the work done by 1 woman in 1 day = (1/44) / 2 = 1/88 of the work.
- The work done by 3 boys in 1 day = 1/44 of the work, so the work done by 1 boy in 1 day = (1/44) / 3 = 1/132 of the work.

### Step 2: Find the efficiency of 1 man, 1 woman, and 1 boy together
Now, we can express the work done by 1 man, 1 woman, and 1 boy in one day:
- Work done by 1 man in 1 day = 1/44
- Work done by 1 woman in 1 day = 1/88
- Work done by 1 boy in 1 day = 1/132

To find the total work done by them in one day, we need to add these fractions:
\[ \text{Total work in 1 day} = \frac{1}{44} + \frac{1}{88} + \frac{1}{132} \]

### Step 3: Find a common denominator
The least common multiple (LCM) of 44, 88, and 132 is 264. We will convert each fraction to have a denominator of 264:
- \(\frac{1}{44} = \frac{6}{264}\)
- \(\frac{1}{88} = \frac{3}{264}\)
- \(\frac{1}{132} = \frac{2}{264}\)

Now, adding these fractions gives:
\[ \text{Total work in 1 day} = \frac{6}{264} + \frac{3}{264} + \frac{2}{264} = \frac{11}{264} \]

### Step 4: Calculate the total work
The total work done is equivalent to the work done by 1 man in 44 days:
\[ \text{Total work} = 1 \text{ (whole work)} = 6 \text{ (the LCM of efficiencies)} \times 44 = 264 \]

### Step 5: Calculate the number of days required for 1 man, 1 woman, and 1 boy 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 use the formula:
\[ \text{Days} = \frac{\text{Total work}}{\text{Work done in 1 day}} = \frac{264}{\frac{11}{264}} = \frac{264 \times 264}{11} = 24 \]

Thus, the same piece of work will be done by 1 man, 1 woman, and 1 boy in **24 days**.