Sixteen men, working at 6 h a day, can do a piece of work in 15 days. In how many days can 18 men working at 10 h a day do the same work?

Options

A. 18
B. 10
C. 16
D. 8

Answer

To solve the problem step by step, we will use the information given in the question and apply the concept of work done, which is based on the number of workers, hours worked, and the total work.

### Step 1: Calculate the total work done by 16 men in 15 days.
- **Given:** 16 men work for 6 hours a day for 15 days.
- **Work done by 1 man in 1 hour:** Let’s denote the work done by 1 man in 1 hour as \(x\).
- **Work done by 16 men in 1 hour:** \(16 \times x = 16x\).
- **Work done by 16 men in 6 hours (1 day):**
\[ 6 \text{ hours} \times 16x = 96x \]
- **Work done by 16 men in 15 days:**
\[ 15 \text{ days} \times 96x = 1440x \]
Thus, the total work \(W\) is \(1440x\).

### Step 2: Calculate the work done by 18 men in 1 day.
- **Given:** 18 men working for 10 hours a day.
- **Work done by 18 men in 1 hour:**
\[ 18 \times x = 18x \]
- **Work done by 18 men in 10 hours (1 day):**
\[ 10 \text{ hours} \times 18x = 180x \]

### Step 3: Set up the equation to find the number of days \(T\) needed for 18 men to complete the work.
- **Work done by 18 men in \(T\) days:**
\[ T \times 180x \]
- **Since this work must equal the total work \(W\):**
\[ T \times 180x = 1440x \]

### Step 4: Solve for \(T\).
- **Cancel \(x\) from both sides:**
\[ T \times 180 = 1440 \]
- **Divide both sides by 180:**
\[ T = \frac{1440}{180} \]
- **Simplifying the fraction:**
\[ T = 8 \]

### Conclusion:
Therefore, 18 men working at 10 hours a day can complete the work in **8 days**.

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