if the manufacture gains `10%` the wholesale dealer `15%` and the retailer `25%` then what is the production cost of a washing machine whose retails price is `₹37950`?

Options

A. `26,000`
B. `20,000`
C. `24,000`
D. `21,000`

Answer

To find the production cost of the washing machine whose retail price is ₹37,950, we need to work backwards through the profit percentages of the manufacturer, wholesaler, and retailer.

### Step-by-Step Solution:

1. **Identify the Retail Price (RP)**:
The retail price of the washing machine is given as ₹37,950.

2. **Understand the Profit Percentages**:
- Retailer gains 25%
- Wholesaler gains 15%
- Manufacturer gains 10%

3. **Calculate the Selling Price for the Retailer (SP_Retailer)**:
The selling price for the retailer can be expressed as:
\[ SP_{Retailer} = CP_{Retailer} \times (1 + \frac{Profit\%}{100}) = CP_{Retailer} \times 1.25 \]
Therefore, we can express the cost price for the retailer (CP_Retailer) as:
\[ CP_{Retailer} = \frac{SP_{Retailer}}{1.25} \]

4. **Calculate the Cost Price for the Retailer**:
Using the retail price:
\[ CP_{Retailer} = \frac{37,950}{1.25} = 30,360 \]

5. **Calculate the Selling Price for the Wholesaler (SP_Wholesaler)**:
The selling price for the wholesaler can be expressed as:
\[ SP_{Wholesaler} = CP_{Wholesaler} \times (1 + \frac{Profit\%}{100}) = CP_{Wholesaler} \times 1.15 \]
Therefore, we can express the cost price for the wholesaler (CP_Wholesaler) as:
\[ CP_{Wholesaler} = \frac{SP_{Wholesaler}}{1.15} \]

6. **Calculate the Cost Price for the Wholesaler**:
Using the cost price for the retailer:
\[ CP_{Wholesaler} = \frac{30,360}{1.15} = 26,420 \]

7. **Calculate the Selling Price for the Manufacturer (SP_Manufacturer)**:
The selling price for the manufacturer can be expressed as:
\[ SP_{Manufacturer} = CP_{Manufacturer} \times (1 + \frac{Profit\%}{100}) = CP_{Manufacturer} \times 1.10 \]
Therefore, we can express the cost price for the manufacturer (CP_Manufacturer) as:
\[ CP_{Manufacturer} = \frac{SP_{Manufacturer}}{1.10} \]

8. **Calculate the Production Cost of the Washing Machine**:
Using the cost price for the wholesaler:
\[ CP_{Manufacturer} = \frac{26,420}{1.10} = 24,018.18 \]

### Final Answer:
The production cost of the washing machine is approximately **₹24,018.18**.