By selling a T-shirt for Rs. 648, a shopkeeper loses 4%. For how much should he sell it to gain 4%

Answer

To solve the problem step by step, we will first find the cost price (CP) of the T-shirt using the information given about the selling price (SP) and the loss percentage. Then, we will calculate the new selling price required to achieve a gain of 4%.

### Step 1: Calculate the Cost Price (CP)
We know that the shopkeeper sold the T-shirt for Rs. 648 and incurred a loss of 4%.

The formula to calculate the cost price when there is a loss is:
\[ CP = \frac{100}{100 - \text{Loss \%}} \times SP \]

Substituting the values:
\[ CP = \frac{100}{100 - 4} \times 648 \]
\[ CP = \frac{100}{96} \times 648 \]

Now, we will calculate this:
\[ CP = \frac{100 \times 648}{96} \]
\[ CP = \frac{64800}{96} \]
\[ CP = 675 \]

### Step 2: Calculate the New Selling Price for a Gain of 4%
Now that we have the cost price (CP = Rs. 675), we need to find the selling price (SP) that would give a gain of 4%.

The formula to calculate the selling price when there is a gain is:
\[ SP = \frac{100 + \text{Gain \%}}{100} \times CP \]

Substituting the values:
\[ SP = \frac{100 + 4}{100} \times 675 \]
\[ SP = \frac{104}{100} \times 675 \]

Now, we will calculate this:
\[ SP = 1.04 \times 675 \]
\[ SP = 702 \]

### Final Answer
The shopkeeper should sell the T-shirt for Rs. 702 to gain 4%.

---