On selling an article for Rs.48 a shopkeeper loses 20%. In order to gain 20%, what would the selling price?

Options

A. Rs.52
B. Rs.56
C. Rs.68
D. Rs.72

Answer

To solve the problem step by step, we will follow the process outlined in the video transcript.

### Step 1: Understand the given information
The shopkeeper sells an article for Rs. 48 and incurs a loss of 20%. We need to find the selling price at which he would gain a profit of 20%.

### Step 2: Calculate the Cost Price (CP)
To find the Cost Price when there is a loss, we can use the formula:
\[ CP = \frac{SP \times 100}{100 - \text{Loss Percentage}} \]
Here, the Selling Price (SP) is Rs. 48 and the Loss Percentage is 20%.

Substituting the values into the formula:
\[ CP = \frac{48 \times 100}{100 - 20} = \frac{4800}{80} = 60 \]
So, the Cost Price (CP) is Rs. 60.

### Step 3: Calculate the Profit for a 20% gain
To find the Selling Price (SP) for a 20% gain, we first need to calculate the profit. The profit can be calculated using the formula:
\[ \text{Profit} = \text{Profit Percentage} \times CP \]
The Profit Percentage is 20%, and we already calculated CP as Rs. 60. Therefore:
\[ \text{Profit} = \frac{20}{100} \times 60 = 12 \]
So, the profit is Rs. 12.

### Step 4: Calculate the new Selling Price (SP)
Now we can find the new Selling Price using the formula:
\[ SP = CP + \text{Profit} \]
Substituting the values we have:
\[ SP = 60 + 12 = 72 \]
Thus, the Selling Price for a 20% gain would be Rs. 72.

### Final Answer
The selling price at which the shopkeeper would gain 20% is Rs. 72.

---