If the manufacturer gains 6% the wholesale dealer 8% and the retailer10% then what is the producation cost of the geyser br ₹15741.

Answer

To find the production cost of the geyser given the selling price and the profits at each stage, we can follow these steps:

### Step-by-Step Solution:

1. **Let the Production Cost be X**:
We denote the production cost of the geyser as \( X \).

2. **Calculate the Selling Price after Manufacturer's Profit**:
The manufacturer gains 6% on the production cost. Therefore, the selling price (SP) after the manufacturer's profit is calculated as:
\[ SP_{\text{manufacturer}} = X + 6\% \text{ of } X = X + \frac{6}{100}X = \frac{106}{100}X = \frac{53}{50}X \]

3. **Calculate the Selling Price after Wholesale Dealer's Profit**:
The wholesale dealer gains 8% on the selling price from the manufacturer. Thus, the selling price after the wholesale dealer's profit is:
\[ SP_{\text{wholesale}} = SP_{\text{manufacturer}} + 8\% \text{ of } SP_{\text{manufacturer}} = \frac{53}{50}X + \frac{8}{100} \cdot \frac{53}{50}X \]
\[ = \frac{53}{50}X + \frac{4.24}{50}X = \frac{53 + 4.24}{50}X = \frac{57.24}{50}X \]

4. **Calculate the Selling Price after Retailer's Profit**:
The retailer gains 10% on the selling price from the wholesale dealer. Therefore, the final selling price is:
\[ SP_{\text{retailer}} = SP_{\text{wholesale}} + 10\% \text{ of } SP_{\text{wholesale}} = \frac{57.24}{50}X + \frac{10}{100} \cdot \frac{57.24}{50}X \]
\[ = \frac{57.24}{50}X + \frac{5.724}{50}X = \frac{57.24 + 5.724}{50}X = \frac{62.964}{50}X \]

5. **Set the Final Selling Price Equal to ₹15741**:
According to the problem, the final selling price is ₹15741. Therefore, we can set up the equation:
\[ \frac{62.964}{50}X = 15741 \]

6. **Solve for X**:
To find \( X \), we can rearrange the equation:
\[ X = 15741 \cdot \frac{50}{62.964} \]
\[ X = 15741 \cdot 0.794 = 12500 \]

7. **Conclusion**:
The production cost of the geyser is ₹12500.