The ratio of selling price of 3 articles A, B, C is 8 : 9 : 5 and ratio of their profit % is 8 : 7 : 14. If profit % of A is 14.28% and CP of B is Rs 400. Find overall%.

Answer

To solve the problem step by step, we will follow the given information and calculate the required values.

### Step 1: Understand the Ratios
We are given the selling price (SP) ratios of articles A, B, and C as:
- SP of A : SP of B : SP of C = 8 : 9 : 5

Let the SPs be:
- SP of A = 8X
- SP of B = 9X
- SP of C = 5X

### Step 2: Profit Percentage Ratios
We are also given the profit percentage ratios as:
- Profit % of A : Profit % of B : Profit % of C = 8 : 7 : 14

Let the profit percentages be:
- Profit % of A = 8Y
- Profit % of B = 7Y
- Profit % of C = 14Y

### Step 3: Find the Value of Y
We know that the profit percentage of A is given as 14.28%. Therefore, we can set up the equation:
\[ 8Y = 14.28 \]
To find Y:
\[ Y = \frac{14.28}{8} = 1.785 \]

### Step 4: Calculate Profit Percentages
Now we can calculate the profit percentages for B and C:
- Profit % of B = 7Y = 7 * 1.785 = 12.495% (approximately 12.5%)
- Profit % of C = 14Y = 14 * 1.785 = 24.99% (approximately 25%)

### Step 5: Find the Cost Price (CP) of B
We are given that the cost price (CP) of B is Rs 400. We can find the selling price (SP) of B using the profit percentage:
\[ SP = CP + (Profit \% \times CP) \]
\[ SP = 400 + (12.5\% \times 400) \]
\[ SP = 400 + \frac{12.5}{100} \times 400 = 400 + 50 = 450 \]

### Step 6: Calculate SP of A and C
From the SP ratios:
- SP of B = 9X = 450
Thus,
\[ X = \frac{450}{9} = 50 \]
Now we can find SP of A and C:
- SP of A = 8X = 8 * 50 = 400
- SP of C = 5X = 5 * 50 = 250

### Step 7: Calculate CP of A and C
Using the profit percentages:
- For A (Profit % = 14.28%):
\[ SP = CP + (Profit \% \times CP) \]
Let CP of A be \( CP_A \):
\[ 400 = CP_A + \frac{14.28}{100} \times CP_A \]
\[ 400 = CP_A \left(1 + \frac{14.28}{100}\right) \]
\[ 400 = CP_A \left(\frac{114.28}{100}\right) \]
\[ CP_A = \frac{400 \times 100}{114.28} \approx 350 \]

- For C (Profit % = 25%):
Let CP of C be \( CP_C \):
\[ SP = CP_C + (25\% \times CP_C) \]
\[ 250 = CP_C + \frac{25}{100} \times CP_C \]
\[ 250 = CP_C \left(1 + \frac{25}{100}\right) \]
\[ 250 = CP_C \left(\frac{125}{100}\right) \]
\[ CP_C = \frac{250 \times 100}{125} = 200 \]

### Step 8: Calculate Total CP and Total SP
Now we can find the total CP and total SP:
- Total CP = CP of A + CP of B + CP of C
\[ Total CP = 350 + 400 + 200 = 950 \]

- Total SP = SP of A + SP of B + SP of C
\[ Total SP = 400 + 450 + 250 = 1100 \]

### Step 9: Calculate Overall Profit and Profit Percentage
Overall Profit:
\[ Overall Profit = Total SP - Total CP = 1100 - 950 = 150 \]

Profit Percentage:
\[ Profit \% = \left(\frac{Overall Profit}{Total CP}\right) \times 100 \]
\[ Profit \% = \left(\frac{150}{950}\right) \times 100 \approx 15.79\% \]

### Final Answer:
The overall profit percentage is approximately **15.79%**.