The marked price of an article is rs 400. After allowing a discount of 20% on the marked price, a shopkeeper makes profit rs 32. His gain percent is :

Options

A. 9
B. `11 1/9`
C. `12 1/9`
D. 8

Answer

To solve the problem step by step, we will calculate the selling price after the discount, find the cost price using the profit information, and then calculate the gain percentage.

### Step 1: Calculate the Selling Price (SP)
The marked price (MP) of the article is given as Rs 400, and a discount of 20% is allowed on this marked price.

\[ \text{Discount} = \frac{20}{100} \times \text{MP} = \frac{20}{100} \times 400 = 80 \]

Now, we can calculate the selling price (SP):

\[ \text{SP} = \text{MP} - \text{Discount} = 400 - 80 = 320 \]

### Step 2: Calculate the Cost Price (CP)
We know that the shopkeeper makes a profit of Rs 32. The relationship between selling price, cost price, and profit is given by:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Substituting the known values:

\[ 320 = \text{CP} + 32 \]

To find the cost price (CP), we rearrange the equation:

\[ \text{CP} = 320 - 32 = 288 \]

### Step 3: Calculate the Gain Percentage
The gain percentage can be calculated using the formula:

\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Gain} = 32, \quad \text{CP} = 288 \]

\[ \text{Gain Percentage} = \left( \frac{32}{288} \right) \times 100 \]

Calculating this gives:

\[ \text{Gain Percentage} = \left( \frac{32}{288} \right) \times 100 = \frac{3200}{288} \approx 11.11\% \]

### Final Answer
The gain percentage is approximately \( 11 \frac{1}{9}\% \).

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