By selling a towel for Rs `126.90`, a draper loses `6%`. For how much should he sell the towel to gain `4%`?

Answer

To solve the problem step by step, we will first find the cost price of the towel using the information given about the selling price and the loss percentage. Then, we will calculate the selling price required to achieve a gain of 4%.

### Step 1: Identify the given values
- Selling Price (SP) = Rs 126.90
- Loss Percentage = 6%

### Step 2: Calculate the Cost Price (CP)
To find the cost price when there is a loss, we can use the formula:
\[ CP = \frac{100}{100 - \text{Loss Percentage}} \times SP \]
Substituting the values:
\[ CP = \frac{100}{100 - 6} \times 126.90 \]
\[ CP = \frac{100}{94} \times 126.90 \]

### Step 3: Simplify the calculation
Calculating the above expression:
\[ CP = \frac{100 \times 126.90}{94} \]
\[ CP = \frac{12690}{94} \approx 135 \]
So, the Cost Price (CP) is Rs 135.

### Step 4: Calculate the Selling Price for a 4% gain
Now, we want to find the selling price that would give a gain of 4%. The formula for selling price when there is a gain is:
\[ SP = CP \times \left(1 + \frac{\text{Gain Percentage}}{100}\right) \]
Substituting the values:
\[ SP = 135 \times \left(1 + \frac{4}{100}\right) \]
\[ SP = 135 \times \left(1 + 0.04\right) \]
\[ SP = 135 \times 1.04 \]

### Step 5: Simplify the calculation
Calculating the above expression:
\[ SP = 140.4 \]
So, the required selling price to gain 4% is Rs 140.40.

### Final Answer:
The draper should sell the towel for Rs 140.40 to gain 4%.

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