By selling a sofa-set for Rs 2,500, the shopkeeper loses 20%. Find his loss percent or profit percent, if he sells the same sofa-set for Rs 3,150.

Answer

To solve the problem step by step, we need to find the cost price of the sofa set first and then determine the profit percentage when it is sold for Rs 3,150.

### Step 1: Find the Cost Price (CP)

Given:
- Selling Price (SP) = Rs 2,500
- Loss Percentage = 20%

We can use the formula for calculating the cost price when there is a loss:

\[ \text{Cost Price (CP)} = \frac{100}{100 - \text{Loss Percentage}} \times \text{Selling Price (SP)} \]

Substituting the values:

\[ \text{CP} = \frac{100}{100 - 20} \times 2500 \]

\[ \text{CP} = \frac{100}{80} \times 2500 \]

\[ \text{CP} = \frac{5}{4} \times 2500 \]

Calculating this gives:

\[ \text{CP} = \frac{5 \times 2500}{4} = \frac{12500}{4} = 3125 \]

### Step 2: Calculate the Gain when Selling Price is Rs 3,150

Now, we have:
- Selling Price (SP) = Rs 3,150
- Cost Price (CP) = Rs 3,125

To find the gain:

\[ \text{Gain} = \text{SP} - \text{CP} \]

Substituting the values:

\[ \text{Gain} = 3150 - 3125 = 25 \]

### Step 3: Calculate the Gain Percentage

The formula for gain percentage is:

\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 \]

Substituting the values:

\[ \text{Gain Percentage} = \left(\frac{25}{3125}\right) \times 100 \]

Calculating this gives:

\[ \text{Gain Percentage} = \frac{25 \times 100}{3125} = \frac{2500}{3125} \]

Now, simplifying:

\[ \text{Gain Percentage} = 0.8 \times 100 = 0.8\% \]

### Final Answer

The shopkeeper will have a gain of **0.8%** when selling the sofa set for Rs 3,150.

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