Cost price of an article is 39% less than the marked price of the article and shopkeeper earned 40% profit in selling the article. If amount of profit is Rs 196 more than amount of discount, then find cost price of article.

Options

A. Rs 1220
B. Rs 1225
C. Rs 1298
D. Rs 1260

Answer

To solve the problem step by step, we will follow the information given in the question and derive the required values.

### Step 1: Define Variables
Let the marked price (MP) of the article be represented as \( MP = 100 \) (for simplicity).

### Step 2: Calculate Cost Price (CP)
Since the cost price is 39% less than the marked price, we can calculate the cost price as follows:
\[ CP = MP - 39\% \text{ of } MP = 100 - 39 = 61 \]

### Step 3: Calculate Selling Price (SP)
The shopkeeper earns a profit of 40% on the cost price. Thus, the selling price can be calculated as:
\[ SP = CP + 40\% \text{ of } CP = 61 + 0.4 \times 61 = 61 + 24.4 = 85.4 \]

### Step 4: Calculate Profit
Profit is defined as the difference between the selling price and the cost price:
\[ \text{Profit} = SP - CP = 85.4 - 61 = 24.4 \]

### Step 5: Calculate Discount
The discount can be calculated as the difference between the marked price and the selling price:
\[ \text{Discount} = MP - SP = 100 - 85.4 = 14.6 \]

### Step 6: Set Up the Equation
According to the problem, the amount of profit is Rs. 196 more than the amount of discount:
\[ \text{Profit} = \text{Discount} + 196 \]
Substituting the values we have:
\[ 24.4 = 14.6 + 196 \]

### Step 7: Calculate the Value of 1
To find the value of 1, we can set up the equation based on the difference between profit and discount:
\[ \text{Profit} - \text{Discount} = 196 \]
This gives us:
\[ 24.4 - 14.6 = 196 \]
Calculating the left side:
\[ 9.8 = 196 \]

### Step 8: Find the Value of 1
Now, we can find the value of 1:
\[ \text{Value of 1} = \frac{196}{9.8} = 20 \]

### Step 9: Calculate the Cost Price
Since we have established that the cost price is represented as 61 in our initial assumption, we can find the actual cost price:
\[ \text{Actual CP} = 61 \times 20 = 1220 \]

### Final Answer
Thus, the cost price of the article is:
\[ \text{Cost Price} = Rs. 1220 \]

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