5 men can prepare 10 toys in 6 days working 6 hours a day. Then a how many days can 12 men prepare 16 toys working 8 hrs a day?

Options

A. 5 days
B. 3 days
C. 4 days
D. 6 days

Answer

To solve the problem step by step, we will use the formula for work done by people over time, which relates the number of people, the number of days, the number of hours worked, and the efficiency.

### Step 1: Understand the given information
We know that:
- 5 men can prepare 10 toys in 6 days, working 6 hours a day.

### Step 2: Calculate the total work done in terms of man-hours
Total work done (in man-hours) can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Number of Hours per Day} \]

For the first condition:
\[ \text{Total Work} = 5 \text{ men} \times 6 \text{ days} \times 6 \text{ hours/day} = 180 \text{ man-hours} \]

### Step 3: Determine the work required for the second condition
Now, we need to find out how many days it will take for 12 men to prepare 16 toys working 8 hours a day.

### Step 4: Calculate the total work required for the second condition
Using the same formula, we can express the work required for the second condition:
Let \( d \) be the number of days required.
\[ \text{Total Work} = 12 \text{ men} \times d \text{ days} \times 8 \text{ hours/day} = 96d \text{ man-hours} \]

### Step 5: Set up the equation
Since the total work required to prepare 10 toys is equal to the total work required to prepare 16 toys, we can set the two equations equal to each other:
\[ 180 \text{ man-hours} = 96d \text{ man-hours} \]

### Step 6: Solve for \( d \)
Now, we can solve for \( d \):
\[ d = \frac{180}{96} \]

### Step 7: Simplify the fraction
To simplify \( \frac{180}{96} \):
\[ d = \frac{180 \div 12}{96 \div 12} = \frac{15}{8} = 1.875 \text{ days} \]

### Step 8: Calculate the total days required
Since we need to prepare 16 toys, we can find the total days required by scaling up:
\[ d = \frac{16 \text{ toys}}{10 \text{ toys}} \times 1.875 = 3 \text{ days} \]

### Final Answer
Thus, it will take **3 days** for 12 men to prepare 16 toys working 8 hours a day.

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