A towel is sold for Rs. 198 at a gain of 10%. What is the cost price of the towel ? At price must it be sold be gain 25%?

Answer

To solve the problem step by step, we will first find the cost price of the towel and then determine the selling price for a 25% gain.

### Step 1: Identify the given information
- Selling Price (SP) = Rs. 198
- Gain = 10%

### Step 2: Use the formula to find the Cost Price (CP)
The formula to find the Cost Price when the Selling Price and Gain are known is:
\[ CP = \frac{SP \times 100}{100 + \text{Gain}} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ CP = \frac{198 \times 100}{100 + 10} \]
\[ CP = \frac{198 \times 100}{110} \]

### Step 4: Calculate the Cost Price
Now, we will calculate the cost price:
\[ CP = \frac{19800}{110} \]
\[ CP = 180 \]
Thus, the cost price of the towel is Rs. 180.

### Step 5: Calculate the new Selling Price for a 25% gain
To find the new selling price with a 25% gain, we will use the formula:
\[ \text{New SP} = CP \times \left(1 + \frac{\text{New Gain}}{100}\right) \]
Where the new gain is 25%.

### Step 6: Substitute the values into the formula
Substituting the known values:
\[ \text{New SP} = 180 \times \left(1 + \frac{25}{100}\right) \]
\[ \text{New SP} = 180 \times \left(1 + 0.25\right) \]
\[ \text{New SP} = 180 \times 1.25 \]

### Step 7: Calculate the New Selling Price
Now, we will calculate the new selling price:
\[ \text{New SP} = 180 \times 1.25 = 225 \]
Thus, the towel must be sold for Rs. 225 to gain 25%.

### Final Answers:
- Cost Price of the towel = Rs. 180
- New Selling Price for 25% gain = Rs. 225

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