Solving Manufacturer's Cost Price Calculation

This problem involves calculating the initial cost price for a manufacturer given a series of markups (profits) at different stages of the supply chain. We are given the final price paid by the customer and the profit percentages made by the manufacturer, wholesaler, and retailer.

Understanding Profit Calculations

Profit is calculated as a percentage of the cost price. If an item is sold at a profit of $P\%$, the selling price ($SP$) is related to the cost price ($CP$) by the formula:

$SP = CP \times \left(1 + \frac{P}{100}\right)$

To find the cost price when the selling price and profit percentage are known, we rearrange the formula:

$CP = \frac{SP}{\left(1 + \frac{P}{100}\right)}$

Step-by-Step Solution

We need to work backward from the customer's price to find the manufacturer's original cost price. Let:

• $C_M$ = Cost Price for the Manufacturer
• $SP_M$ = Selling Price for the Manufacturer (also Cost Price for the Wholesaler, $C_W$)
• $SP_W$ = Selling Price for the Wholesaler (also Cost Price for the Retailer, $C_R$)
• $SP_R$ = Selling Price for the Retailer (also the price paid by the Customer)

Step 1: Calculate the Retailer's Cost Price ($C_R$)

The retailer sells the product to the customer at a profit of 25%. The customer pays ₹714 ($SP_R$).

Using the formula $SP = CP \times (1 + P/100)$:

$SP_R = C_R \times \left(1 + \frac{25}{100}\right)$

$714 = C_R \times \left(1 + 0.25\right)$

$714 = C_R \times 1.25$

Now, solve for $C_R$:

$C_R = \frac{714}{1.25}$

$C_R = \frac{714}{\frac{5}{4}} = 714 \times \frac{4}{5} = \frac{2856}{5}$

$C_R = 571.2$

So, the retailer's cost price was ₹571.20.

Step 2: Calculate the Wholesaler's Cost Price ($C_W$)

The wholesaler sells the product to the retailer at a profit of 60%. The wholesaler's selling price ($SP_W$) is the retailer's cost price ($C_R$), which we found to be ₹571.20.

Using the formula $SP = CP \times (1 + P/100)$:

$SP_W = C_W \times \left(1 + \frac{60}{100}\right)$

$571.20 = C_W \times \left(1 + 0.60\right)$

$571.20 = C_W \times 1.60$

Now, solve for $C_W$:

$C_W = \frac{571.20}{1.60} = \frac{571.2}{1.6}$

$C_W = \frac{5712}{16}$

$C_W = 357$

So, the wholesaler's cost price was ₹357.

Step 3: Calculate the Manufacturer's Cost Price ($C_M$)

The manufacturer sells the product to the wholesaler at a profit of 40%. The manufacturer's selling price ($SP_M$) is the wholesaler's cost price ($C_W$), which we found to be ₹357.

Using the formula $SP = CP \times (1 + P/100)$:

$SP_M = C_M \times \left(1 + \frac{40}{100}\right)$

$357 = C_M \times \left(1 + 0.40\right)$

$357 = C_M \times 1.40$

Now, solve for $C_M$:

$C_M = \frac{357}{1.40} = \frac{357}{1.4}$

$C_M = \frac{3570}{14}$

$C_M = 255$

Therefore, the cost price for the manufacturer was ₹255.

Summary of Calculations

The cost price for the manufacturer is ₹255.