A shopkeeper fixes the price of an article in such a way that after allowing 32% discount, be wants a gain of 14%. If the marked price is Rs. 342, then the cost price of the article is:

Options

A. Rs. 212
B. Rs. 196
C. Rs. 204
D. Rs. 218

Answer

To solve the problem step-by-step, we will follow the logical sequence outlined in the video transcript:

### Step 1: Identify the given values
- Marked Price (MP) = Rs. 342
- Discount = 32%
- Desired Profit = 14%

### Step 2: Calculate the Selling Price (SP) after discount
The Selling Price can be calculated using the formula:
\[ SP = MP - (Discount \% \times MP) \]
First, we need to calculate the amount of discount:
\[ Discount \, Amount = \frac{32}{100} \times 342 = 109.44 \]
Now, we can find the Selling Price:
\[ SP = 342 - 109.44 = 232.56 \]

### Step 3: Relate Selling Price to Cost Price
We know that the Selling Price (SP) is also related to the Cost Price (CP) through the profit percentage. The formula for profit is:
\[ Profit \% = \frac{SP - CP}{CP} \times 100 \]
Given that the profit percentage is 14%, we can set up the equation:
\[ 14 = \frac{232.56 - CP}{CP} \times 100 \]

### Step 4: Rearranging the equation to find CP
We can rearrange the equation to isolate CP:
\[ \frac{232.56 - CP}{CP} = \frac{14}{100} \]
Cross-multiplying gives:
\[ 100(232.56 - CP) = 14 \times CP \]
Expanding this:
\[ 23256 - 100CP = 14CP \]
Combining like terms:
\[ 23256 = 100CP + 14CP \]
\[ 23256 = 114CP \]

### Step 5: Solve for CP
Now, we can solve for CP:
\[ CP = \frac{23256}{114} \]
Calculating this gives:
\[ CP = 204 \]

### Final Answer
The cost price of the article is Rs. 204.

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