The profit percentage on the three articles A, B and C is 10%, 20% and 25% and the ratio of the cost prices is 1 : 2 : 4. Also the ratio of number of articles sodl of A, B and C is 2 : 5 : 2 then the overall profit percentage is.

Answer

To find the overall profit percentage for articles A, B, and C, we will follow these steps:

### Step 1: Determine the Cost Prices
Given the ratio of the cost prices of articles A, B, and C is 1:2:4, let's assume:
- Cost Price of A = x
- Cost Price of B = 2x
- Cost Price of C = 4x

### Step 2: Calculate the Total Cost Price
The total cost price (CP) of the three articles can be calculated as:
\[ \text{Total CP} = x + 2x + 4x = 7x \]

### Step 3: Determine the Selling Prices
Next, we calculate the selling prices (SP) based on the profit percentages:
- Profit Percentage of A = 10% → SP of A = CP of A + 10% of CP of A = \( x + 0.1x = 1.1x \)
- Profit Percentage of B = 20% → SP of B = CP of B + 20% of CP of B = \( 2x + 0.2(2x) = 2x + 0.4x = 2.4x \)
- Profit Percentage of C = 25% → SP of C = CP of C + 25% of CP of C = \( 4x + 0.25(4x) = 4x + 1x = 5x \)

### Step 4: Determine the Number of Articles Sold
Given the ratio of the number of articles sold is 2:5:2, let's assume:
- Number of articles sold of A = 2k
- Number of articles sold of B = 5k
- Number of articles sold of C = 2k

### Step 5: Calculate Total Selling Prices
Now we can calculate the total selling price (SP) for each article:
- Total SP of A = Number of articles sold × SP of A = \( 2k \times 1.1x = 2.2kx \)
- Total SP of B = Number of articles sold × SP of B = \( 5k \times 2.4x = 12kx \)
- Total SP of C = Number of articles sold × SP of C = \( 2k \times 5x = 10kx \)

### Step 6: Calculate Total Selling Price
The total selling price (TSP) is:
\[ \text{Total SP} = 2.2kx + 12kx + 10kx = (2.2k + 12k + 10k)x = 24.2kx \]

### Step 7: Calculate Total Profit
Total Profit can be calculated as:
\[ \text{Total Profit} = \text{Total SP} - \text{Total CP} = 24.2kx - 7x \]

### Step 8: Calculate Overall Profit Percentage
The overall profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Total Profit}}{\text{Total CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{(24.2k - 7)x}{7x} \right) \times 100 = \left( \frac{24.2k - 7}{7} \right) \times 100 \]

### Step 9: Simplify
To find the overall profit percentage, we need to evaluate \( k \). Since \( k \) is a common factor, it will cancel out when calculating the percentage. Therefore:
\[ \text{Profit Percentage} = \left( \frac{24.2 - 1}{7} \right) \times 100 = \left( \frac{23.2}{7} \right) \times 100 \approx 331.43\% \]

### Final Calculation
Calculating the final value gives us:
\[ \text{Overall Profit Percentage} \approx 23.2\% \]

Thus, the overall profit percentage is approximately **23.2%**.