If 15 men can complete a work in 16 days by working 8 hours daily, then in how many days will 10 men complete the work by working 12 hours daily?

Options

A. a) 15
B. b) 12
C. c) 10
D. d) 16

Answer

To solve the problem, we will use the concept of man-hours, which is the total amount of work done by a certain number of men over a period of time.

### Step-by-Step Solution:

1. **Calculate Total Work in Man-Hours:**
- Given that 15 men can complete the work in 16 days by working 8 hours daily.
- Total work (in man-hours) = Number of men × Number of days × Number of hours per day
- Total work = 15 men × 16 days × 8 hours/day = 1920 man-hours

2. **Set Up the Equation for 10 Men Working 12 Hours Daily:**
- Let the number of days required for 10 men to complete the work be \( D_2 \).
- The total work can also be expressed as:
- Total work = Number of men × Number of days × Number of hours per day
- Total work = 10 men × \( D_2 \) days × 12 hours/day

3. **Equate the Total Work:**
- Since the total work remains the same, we can set the two expressions for total work equal to each other:
- \( 1920 = 10 \times D_2 \times 12 \)

4. **Solve for \( D_2 \):**
- Simplifying the equation:
- \( 1920 = 120 \times D_2 \)
- Now, divide both sides by 120:
- \( D_2 = \frac{1920}{120} = 16 \)

5. **Conclusion:**
- Therefore, 10 men will complete the work in 16 days by working 12 hours daily.

### Final Answer:
10 men will complete the work in **16 days**.

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