34 men can do a piece of work in 12 days . How many days will 51 men take to do it

Options

A. a) 8
B. b) 5
C. c) 10
D. d) 6

Answer

To solve the problem step by step, we can use the concept of work, which is defined as the product of the number of men and the number of days they work.

### Step-by-Step Solution:

1. **Understand the Work Equation**:
The formula for work is given by:
\[ \text{Work} = \text{Number of Men} \times \text{Number of Days} \]

2. **Calculate the Total Work Done by 34 Men**:
Given that 34 men can complete the work in 12 days, we can calculate the total work (W) as follows:
\[ W = 34 \text{ men} \times 12 \text{ days} = 408 \text{ man-days} \]

3. **Set Up the Equation for 51 Men**:
Now, we need to find out how many days (let's call it X) it will take for 51 men to complete the same amount of work. Using the work formula again:
\[ W = 51 \text{ men} \times X \text{ days} \]

4. **Equate the Two Expressions for Work**:
Since the total work done remains the same, we can set the two expressions for work equal to each other:
\[ 34 \times 12 = 51 \times X \]

5. **Substitute the Value of Work**:
Substitute the calculated work into the equation:
\[ 408 = 51 \times X \]

6. **Solve for X**:
To find X, divide both sides of the equation by 51:
\[ X = \frac{408}{51} \]
Simplifying this gives:
\[ X = 8 \]

7. **Conclusion**:
Therefore, 51 men will take 8 days to complete the work.

### Final Answer:
51 men will take **8 days** to do the work.

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