The manufacturer of a machine sells it to a trader making a profit of 15% on its manufacturing cost, the trader sells it to the vendor, making a profit of 5% and vendor sell it to the actual user at a profit of 10%. If the actual user pays Rs. 531.30 for it, then find the manufacturing cost.

Options

A. Rs. 400
B. Rs. 800
C. Rs. 600
D. Rs. 360

Answer

To find the manufacturing cost of the machine, we can work backwards from the final selling price that the actual user pays. The actual user pays Rs. 531.30 after the vendor sells it to them at a profit of 10%.

Let's denote:
- Manufacturing Cost = MC
- Selling Price of Manufacturer = SP_M
- Selling Price of Trader = SP_T
- Selling Price of Vendor = SP_V

### Step 1: Calculate the Selling Price of Vendor (SP_V)

The actual user pays Rs. 531.30, which includes a profit of 10% over the vendor's cost price. We can express this as:

\[ SP_V = \text{Cost Price of Vendor} + 10\% \text{ of Cost Price of Vendor} \]

This can be rewritten as:

\[ SP_V = \text{Cost Price of Vendor} \times \frac{110}{100} \]

Let \( CP_V \) be the cost price of the vendor. Then:

\[ 531.30 = CP_V \times \frac{110}{100} \]

To find \( CP_V \):

\[ CP_V = 531.30 \times \frac{100}{110} = 531.30 \times \frac{10}{11} = 483 \]

### Step 2: Calculate the Selling Price of Trader (SP_T)

The vendor sells the machine to the trader at a profit of 5%. Thus:

\[ SP_T = CP_V + 5\% \text{ of } CP_V \]

This can be rewritten as:

\[ SP_T = CP_V \times \frac{105}{100} \]

Substituting \( CP_V = 483 \):

\[ SP_T = 483 \times \frac{105}{100} = 483 \times 1.05 = 507.15 \]

### Step 3: Calculate the Selling Price of Manufacturer (SP_M)

The trader sells the machine to the manufacturer at a profit of 15%. Thus:

\[ SP_M = CP_T + 15\% \text{ of } CP_T \]

This can be rewritten as:

\[ SP_M = CP_T \times \frac{115}{100} \]

Substituting \( CP_T = 507.15 \):

\[ SP_M = 507.15 \times \frac{100}{115} = 507.15 \times \frac{20}{23} = 440.13 \]

### Step 4: Calculate the Manufacturing Cost (MC)

The manufacturing cost is the cost price of the manufacturer. We have already calculated it as:

\[ MC = SP_M \times \frac{100}{115} \]

Substituting \( SP_M = 440.13 \):

\[ MC = 440.13 \times \frac{100}{115} = 440.13 \times \frac{20}{23} = 400 \]

Thus, the manufacturing cost is:

\[ \text{Manufacturing Cost} = Rs. 400 \]

### Summary of Steps:
1. Calculate the cost price of the vendor using the final selling price and profit percentage.
2. Calculate the selling price of the trader using the vendor's cost price and profit percentage.
3. Calculate the selling price of the manufacturer using the trader's cost price and profit percentage.
4. Finally, calculate the manufacturing cost using the selling price of the manufacturer and profit percentage.