An article is sold at a profit of 20%. If both the cost price and selling price were to be Rs 20 less, the profit would be 10% more. Find the cost price of the article.

Options

A. Rs120
B. Rs80
C. Rs60
D. Rs75

Answer

To solve the problem step-by-step, let's define the variables and follow the logic outlined in the video transcript.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( x \) rupees.

### Step 2: Calculate the Selling Price
Since the article is sold at a profit of 20%, the selling price (SP) can be calculated as:
\[ SP = CP + \text{Profit} \]
The profit is 20% of the cost price:
\[ \text{Profit} = 20\% \text{ of } x = \frac{20}{100} \times x = \frac{x}{5} \]
Thus, the selling price becomes:
\[ SP = x + \frac{x}{5} = \frac{5x}{5} + \frac{x}{5} = \frac{6x}{5} \]

### Step 3: Adjust the Cost Price and Selling Price
If both the cost price and selling price are reduced by Rs 20, the new cost price (CP') and new selling price (SP') will be:
\[ CP' = x - 20 \]
\[ SP' = \frac{6x}{5} - 20 \]

### Step 4: Determine the New Profit Percentage
According to the problem, the new profit percentage becomes 30%. The profit percentage is given by:
\[ \text{Profit Percentage} = \frac{SP' - CP'}{CP'} \times 100 \]
Substituting the values we have:
\[ 30 = \frac{\left(\frac{6x}{5} - 20\right) - (x - 20)}{x - 20} \times 100 \]

### Step 5: Simplify the Equation
First, simplify the numerator:
\[ \frac{6x}{5} - 20 - x + 20 = \frac{6x}{5} - x = \frac{6x}{5} - \frac{5x}{5} = \frac{x}{5} \]
Now, substituting this back into the profit percentage equation:
\[ 30 = \frac{\frac{x}{5}}{x - 20} \times 100 \]
This simplifies to:
\[ 30 = \frac{100x}{5(x - 20)} \]
\[ 30 = \frac{20x}{x - 20} \]

### Step 6: Cross Multiply to Solve for x
Cross-multiplying gives:
\[ 30(x - 20) = 20x \]
Expanding this:
\[ 30x - 600 = 20x \]
Rearranging gives:
\[ 30x - 20x = 600 \]
\[ 10x = 600 \]
\[ x = 60 \]

### Step 7: Conclusion
Thus, the cost price of the article is:
\[ \text{Cost Price} = Rs 60 \]