A person earns 12.5% on one article but loss 10% on another article. If the ratio of the cost price of two articles be 4:5. What is the gain/loss on selling two both articles?

Options

A. 1% loss
B. 0.5% gain
C. 0.75% loss
D. Neither gain nor loss

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
We know that:
- The profit on the first article is 12.5%.
- The loss on the second article is 10%.
- The ratio of the cost prices of the two articles is 4:5.

### Step 2: Assign cost prices based on the ratio
Let the cost price of the first article be \( 4x \) and the cost price of the second article be \( 5x \).

### Step 3: Calculate the selling price of the first article
The profit on the first article is 12.5%. This can be expressed as:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Profit can be calculated as:
\[ \text{Profit} = \frac{12.5}{100} \times 4x = \frac{1}{8} \times 4x = \frac{4x}{8} = \frac{x}{2} \]
Thus, the selling price of the first article is:
\[ SP_1 = 4x + \frac{x}{2} = 4x + 0.5x = 4.5x \]

### Step 4: Calculate the selling price of the second article
The loss on the second article is 10%. This can be expressed as:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} - \text{Loss} \]
Loss can be calculated as:
\[ \text{Loss} = \frac{10}{100} \times 5x = \frac{1}{10} \times 5x = \frac{5x}{10} = \frac{x}{2} \]
Thus, the selling price of the second article is:
\[ SP_2 = 5x - \frac{x}{2} = 5x - 0.5x = 4.5x \]

### Step 5: Calculate total cost price and total selling price
Total cost price (CP) of both articles:
\[ \text{Total CP} = 4x + 5x = 9x \]
Total selling price (SP) of both articles:
\[ \text{Total SP} = SP_1 + SP_2 = 4.5x + 4.5x = 9x \]

### Step 6: Determine gain or loss
Now, we compare the total cost price and total selling price:
\[ \text{Total CP} = 9x \quad \text{and} \quad \text{Total SP} = 9x \]
Since the total cost price is equal to the total selling price, there is neither gain nor loss.

### Final Answer
The person neither gains nor loses on selling both articles.

---