If 7 men working 7 hrs a day for each of 7 days produce 7 units of work, then the units of work produced by 5 men working 5 hrs a day for each of 5 days is 25

Options

A. `(25)/(343)`
B. `(125)/(49)`
C. `(49)/(125)`
D. `(343)/(25)`

Answer

To solve the problem, we will use the relationship between the number of men, the number of days, the number of hours, and the amount of work done.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- In the first scenario:
- Number of men (M1) = 7
- Number of days (D1) = 7
- Number of hours per day (H1) = 7
- Work done (W1) = 7 units
- In the second scenario:
- Number of men (M2) = 5
- Number of days (D2) = 5
- Number of hours per day (H2) = 5
- Work done (W2) = ?

2. **Set Up the Work Formula:**
The formula relating the work done is:
\[ \frac{M1 \times D1 \times H1}{W1} = \frac{M2 \times D2 \times H2}{W2} \]

3. **Substitute the Known Values:**
Substitute the values from the first scenario into the formula:
\[ \frac{7 \times 7 \times 7}{7} = \frac{5 \times 5 \times 5}{W2} \]

4. **Simplify the Left Side:**
Calculate the left side:
\[ \frac{7 \times 7 \times 7}{7} = 7 \times 7 = 49 \]

5. **Set Up the Equation:**
Now we have:
\[ 49 = \frac{5 \times 5 \times 5}{W2} \]

6. **Calculate the Right Side:**
Calculate \(5 \times 5 \times 5\):
\[ 5 \times 5 \times 5 = 125 \]

7. **Set Up the Final Equation:**
Now we have:
\[ 49 = \frac{125}{W2} \]

8. **Cross-Multiply to Solve for W2:**
Cross-multiply to find \(W2\):
\[ 49 \times W2 = 125 \]
\[ W2 = \frac{125}{49} \]

9. **Final Answer:**
Thus, the units of work produced by 5 men working 5 hours a day for 5 days is:
\[ W2 = \frac{125}{49} \text{ units} \]