If a manufacturer gains 10 percent, wholesaler 15 percent and retailer 25 per cent, then the production cost of an article, whose retail price is 1,265, Is

Options

A. 1000
B. 750
C. 800
D. 900

Answer

To find the production cost of an article given the retail price and the profits at each stage (manufacturer, wholesaler, and retailer), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Retail Price (RP) = 1265
- Manufacturer's Profit = 10%
- Wholesaler's Profit = 15%
- Retailer's Profit = 25%

2. **Let’s denote the production cost as \( C \)**.

3. **Calculate the Retail Price in terms of the Cost Price for the Retailer**:
- Let the cost price for the retailer be \( R \).
- Since the retailer gains 25%, we can express the retail price as:
\[ RP = R + 0.25R = 1.25R \]
- Therefore, we can express \( R \) as:
\[ R = \frac{RP}{1.25} = \frac{1265}{1.25} \]

4. **Calculate \( R \)**:
- To simplify \( R \):
\[ R = \frac{1265 \times 100}{125} = \frac{126500}{125} = 1012 \]

5. **Now, calculate the Cost Price for the Wholesaler**:
- Let the cost price for the wholesaler be \( W \).
- Since the wholesaler gains 15%, we can express \( R \) as:
\[ R = W + 0.15W = 1.15W \]
- Therefore, we can express \( W \) as:
\[ W = \frac{R}{1.15} = \frac{1012}{1.15} \]

6. **Calculate \( W \)**:
- To simplify \( W \):
\[ W = \frac{1012 \times 100}{115} = \frac{101200}{115} = 880 \]

7. **Now, calculate the Production Cost**:
- Let the production cost be \( C \).
- Since the manufacturer gains 10%, we can express \( W \) as:
\[ W = C + 0.10C = 1.10C \]
- Therefore, we can express \( C \) as:
\[ C = \frac{W}{1.10} = \frac{880}{1.10} \]

8. **Calculate \( C \)**:
- To simplify \( C \):
\[ C = \frac{880 \times 100}{110} = \frac{88000}{110} = 800 \]

### Final Answer:
The production cost of the article is **800**.

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