The cost of labor in manufacturing a product is 16.66% of the total cost. Due to improvements in automation, the cost of labor decreased to 12.5% of total cost, all other cost remaining the same. Find the percentage decrease in the cost of labor.

To calculate the percentage decrease in the cost of labor, we can follow these steps:

### Step 1: Assign Variables
Let the total cost of manufacturing the product be represented by $ C $. Initially, the labor cost was 16.66% of $ C $, and after automation improvements, the labor cost decreased to 12.5% of $ C $.

### Step 2: Calculate Initial and Final Labor Costs
- Initial labor cost: $ \frac{16.66}{100} \times C = 0.1666C $
- Final labor cost: $ \frac{12.5}{100} \times C = 0.125C $

### Step 3: Find the Decrease in Labor Cost
The decrease in labor cost is:
\[
\text{Decrease in labor cost} = 0.1666C - 0.125C = 0.0416C
\]

### Step 4: Find the Percentage Decrease in Labor Cost
The percentage decrease is calculated by dividing the decrease in labor cost by the initial labor cost, and then multiplying by 100:
\[
\text{Percentage decrease} = \left( \frac{0.0416C}{0.1666C} \right) \times 100 = \left( \frac{0.0416}{0.1666} \right) \times 100
\]
\[
\text{Percentage decrease} \approx 24.96\%
\]

### Conclusion:
The percentage decrease in the cost of labor is approximately **24.96%**.

Would you like further details or clarification?

### Related Questions:
1. What is the impact on total cost if labor costs further reduce to 10% of the total cost?
2. How would you calculate the savings in actual dollars if the total cost is $10,000?
3. If automation improvements increase production by 20%, how would this affect labor costs?
4. How do you calculate the total percentage of all other costs combined?
5. What would happen if labor costs increased back to 20% of the total cost?

**Tip:** When dealing with percentages, always express your values clearly in terms of a base amount (like total cost) to simplify calculations.

Discover how to calculate the percentage decrease in labor cost when the labor component of total cost drops from 16.66% to 12.5%. This problem uses basic algebra and percentage decrease formulas, making it suitable for students in Grades 8-10.

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