An article is sold at a profit of 20%. If it had been sold at a profit of 25%, it would have fetched Rs. 35 more. The cost price of the article is :

Options

A. Rs. 650
B. Rs. 700
C. Rs. 750
D. Rs. 800

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define the Cost Price (CP)
Let the cost price (CP) of the article be Rs. 100 (this is a convenient assumption to simplify calculations).

### Step 2: Calculate Selling Price (SP) at 20% Profit
When the article is sold at a profit of 20%, the selling price (SP1) can be calculated as follows:
\[ SP1 = CP + (20\% \text{ of } CP) = 100 + \left(\frac{20}{100} \times 100\right) = 100 + 20 = Rs. 120 \]

### Step 3: Calculate Selling Price (SP) at 25% Profit
Next, we calculate the selling price (SP2) if the article is sold at a profit of 25%:
\[ SP2 = CP + (25\% \text{ of } CP) = 100 + \left(\frac{25}{100} \times 100\right) = 100 + 25 = Rs. 125 \]

### Step 4: Find the Difference in Selling Prices
According to the problem, if the article is sold at a profit of 25%, it would fetch Rs. 35 more than when sold at a profit of 20%. Therefore, we can set up the equation:
\[ SP2 - SP1 = Rs. 35 \]
Substituting the values we calculated:
\[ 125 - 120 = Rs. 5 \]

### Step 5: Relate the Difference to the Cost Price
We know that the difference in selling prices (Rs. 5) corresponds to the difference in profit percentages (from 20% to 25%). Since this difference of Rs. 5 represents a 5% increase in the selling price, we can find the value of 1%:
\[ \text{Value of 1%} = \frac{Rs. 35}{5} = Rs. 7 \]

### Step 6: Calculate the Actual Cost Price
Since we assumed the CP to be Rs. 100, we can find the actual CP:
\[ \text{Actual CP} = 100 \times 7 = Rs. 700 \]

### Final Answer
Thus, the cost price of the article is Rs. 700.