The cost prices of two articles A and B are in the ratio `3 :5` . Rishu earns a profit of `28%` on A and loses `15%` on B. What is her overall loss /gain percent ?

Options

A. Loss , `1.125%`
B. Gain , `1.125%`
C. Gain , `11.25%`
D. Loss , `11.25%`

Answer

To find the overall loss or gain percentage for Rishu, we can follow these steps:

### Step 1: Determine the Cost Prices
The cost prices of articles A and B are in the ratio of 3:5. We can assign values to these cost prices for easier calculations.
Let:
- Cost Price of A (CP_A) = 3x
- Cost Price of B (CP_B) = 5x

### Step 2: Assign a Value for x
For simplicity, we can choose a value for x. Let's assume:
- x = 100
Then:
- CP_A = 3 * 100 = 300
- CP_B = 5 * 100 = 500

### Step 3: Calculate the Selling Price of Article A
Rishu earns a profit of 28% on article A.
To calculate the selling price (SP_A):
\[ \text{Profit on A} = \text{CP_A} \times \frac{28}{100} = 300 \times 0.28 = 84 \]
Thus, the selling price of A:
\[ \text{SP_A} = \text{CP_A} + \text{Profit on A} = 300 + 84 = 384 \]

### Step 4: Calculate the Selling Price of Article B
Rishu incurs a loss of 15% on article B.
To calculate the selling price (SP_B):
\[ \text{Loss on B} = \text{CP_B} \times \frac{15}{100} = 500 \times 0.15 = 75 \]
Thus, the selling price of B:
\[ \text{SP_B} = \text{CP_B} - \text{Loss on B} = 500 - 75 = 425 \]

### Step 5: Calculate Total Selling Price and Total Cost Price
Now, we can calculate the total selling price and total cost price:
- Total Selling Price (SP_total) = SP_A + SP_B
\[ \text{SP_total} = 384 + 425 = 809 \]
- Total Cost Price (CP_total) = CP_A + CP_B
\[ \text{CP_total} = 300 + 500 = 800 \]

### Step 6: Calculate Overall Profit or Loss
Now we can find the overall profit or loss:
\[ \text{Profit} = \text{SP_total} - \text{CP_total} = 809 - 800 = 9 \]

### Step 7: Calculate Profit Percentage
Finally, we can calculate the profit percentage:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP_total}} \right) \times 100 = \left( \frac{9}{800} \right) \times 100 = 1.125\% \]

### Conclusion
Rishu has an overall profit of **1.125%**.

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