If 3 men and 4 boys can do a piece of work in 8 day, then 6 men and 8 boys can do the same work in

Options

A. 2 days
B. 4 days
C. 6 days
D. 16 days

Answer

To solve the problem step by step, we need to find out how many days 6 men and 8 boys can complete the same work that 3 men and 4 boys can do in 8 days.

### Step-by-Step Solution:

1. **Understand the Work Done by 3 Men and 4 Boys**:
- Let the work done by 1 man in 1 day be \( \frac{1}{A} \).
- Let the work done by 1 boy in 1 day be \( \frac{1}{B} \).
- Therefore, the work done by 3 men and 4 boys in one day is:
\[ \text{Work done in 1 day} = 3 \times \frac{1}{A} + 4 \times \frac{1}{B} \]
- Since they complete the work in 8 days, the total work can be expressed as:
\[ \text{Total Work} = \text{Work done in 1 day} \times 8 = 1 \]
- Thus, we have:
\[ 3 \times \frac{1}{A} + 4 \times \frac{1}{B} = \frac{1}{8} \]

2. **Set Up the Equation**:
- Rearranging the equation gives:
\[ 3 \times \frac{1}{A} + 4 \times \frac{1}{B} = \frac{1}{8} \]
- This is our first equation (Equation 1).

3. **Calculate Work Done by 6 Men and 8 Boys**:
- Now, we need to find the work done by 6 men and 8 boys in one day:
\[ \text{Work done in 1 day} = 6 \times \frac{1}{A} + 8 \times \frac{1}{B} \]
- We can multiply Equation 1 by 2 to relate it to this new equation:
\[ 2 \left( 3 \times \frac{1}{A} + 4 \times \frac{1}{B} \right) = 2 \times \frac{1}{8} \]
- This simplifies to:
\[ 6 \times \frac{1}{A} + 8 \times \frac{1}{B} = \frac{1}{4} \]

4. **Determine the Time Taken by 6 Men and 8 Boys**:
- The work done by 6 men and 8 boys in one day is \( \frac{1}{4} \).
- Therefore, the total time taken to complete the work is:
\[ \text{Total Work} = \text{Work done in 1 day} \times \text{Days} \]
- Since the total work is 1, we have:
\[ 1 = \frac{1}{4} \times \text{Days} \]
- Solving for Days gives:
\[ \text{Days} = 4 \]

### Final Answer:
Thus, 6 men and 8 boys can complete the work in **4 days**.