A manufacturer sells his goods to a wholesaler at 10% gain, the whole saler to the retailer at 20% gain and the retailer to the customer at 30% gain. Find what per cent the customer has to pay more on the manufactured price?

Options

A. 0.6
B. 66 `2/3` %
C. 48 `1/5` %
D. 71 `3/5` %

Answer

To solve the problem step by step, we will calculate the selling prices at each stage and find out how much more the customer pays compared to the manufacturer's price.

### Step 1: Calculate the Selling Price of the Manufacturer
Let the manufactured price be \( x \).

The manufacturer sells his goods to the wholesaler at a 10% gain.

The formula for selling price (SP) based on cost price (CP) and gain percentage (G) is:
\[ SP = CP + \left( \frac{G}{100} \times CP \right) \]

For the manufacturer:
\[ SP = x + \left( \frac{10}{100} \times x \right) = x + 0.1x = 1.1x \]

### Step 2: Calculate the Selling Price of the Wholesaler
The wholesaler buys the goods at the selling price of the manufacturer, which is \( 1.1x \). The wholesaler then sells to the retailer at a 20% gain.

Using the same formula:
\[ SP = 1.1x + \left( \frac{20}{100} \times 1.1x \right) = 1.1x + 0.22x = 1.32x \]

### Step 3: Calculate the Selling Price of the Retailer
The retailer buys the goods at the selling price of the wholesaler, which is \( 1.32x \). The retailer sells to the customer at a 30% gain.

Using the formula again:
\[ SP = 1.32x + \left( \frac{30}{100} \times 1.32x \right) = 1.32x + 0.396x = 1.716x \]

### Step 4: Calculate the Percentage Increase from Manufacturer's Price to Customer's Price
Now we need to find out how much more the customer pays compared to the manufacturer's price.

The formula for percentage increase is:
\[ \text{Percentage Increase} = \left( \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \right) \times 100 \]

Here, the final price is \( 1.716x \) and the initial price is \( x \):
\[ \text{Percentage Increase} = \left( \frac{1.716x - x}{x} \right) \times 100 = \left( \frac{0.716x}{x} \right) \times 100 = 71.6\% \]

### Final Answer
The customer has to pay **71.6% more** on the manufactured price.

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