A man loses 10% by selling an article for Rs. 180. At what price should he sell it to gain 10%?

Options

A. ?220
B. X 217.80
C. X 200
D. X 216

Answer

To solve the problem step by step, we need to find the cost price of the article first and then determine the selling price required to achieve a 10% gain.

### Step 1: Determine the Cost Price (CP)

Given that the man sells the article for Rs. 180 and incurs a loss of 10%, we can use the formula for calculating the cost price when there is a loss:

\[ \text{Cost Price (CP)} = \frac{100}{100 - \text{Loss Percentage}} \times \text{Selling Price (SP)} \]

Substituting the values:

\[ \text{CP} = \frac{100}{100 - 10} \times 180 \]

\[ \text{CP} = \frac{100}{90} \times 180 \]

Calculating this:

\[ \text{CP} = \frac{100 \times 180}{90} = \frac{18000}{90} = 200 \]

So, the cost price of the article is Rs. 200.

### Step 2: Calculate the Selling Price for a 10% Gain

Next, we need to find the selling price that would give a 10% gain on the cost price. The formula for calculating the selling price when there is a gain is:

\[ \text{Selling Price (SP)} = \left( \frac{100 + \text{Gain Percentage}}{100} \right) \times \text{Cost Price (CP)} \]

Substituting the values:

\[ \text{SP} = \left( \frac{100 + 10}{100} \right) \times 200 \]

\[ \text{SP} = \left( \frac{110}{100} \right) \times 200 \]

Calculating this:

\[ \text{SP} = 1.1 \times 200 = 220 \]

Thus, to gain 10%, the man should sell the article for Rs. 220.

### Final Answer:
The selling price to gain 10% is Rs. 220.

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