By selling a tape-recorder for Rs. 760, I lose 5%. What percent shall I gain by selling it for Rs. 1000 ?

Options

A. (a) 10%
B. (b) 20%
C. (c) 22%
D. (d) 25%

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Selling Price (SP) and Loss Percentage
- The selling price (SP) of the tape recorder is Rs. 760.
- The loss percentage is 5%.

### Step 2: Calculate the Cost Price (CP)
To find the cost price (CP), we can use the formula:
\[ CP = \frac{SP \times 100}{100 - \text{Loss Percentage}} \]
Substituting the values:
\[ CP = \frac{760 \times 100}{100 - 5} = \frac{760 \times 100}{95} \]
Calculating this gives:
\[ CP = \frac{76000}{95} = 800 \]
So, the cost price (CP) is Rs. 800.

### Step 3: Calculate the Selling Price for the New Scenario
Now, we want to find out the profit percentage when the tape recorder is sold for Rs. 1000.

### Step 4: Calculate the Profit
Profit can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Substituting the values:
\[ \text{Profit} = 1000 - 800 = 200 \]

### Step 5: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{200}{800}\right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \left(\frac{1}{4}\right) \times 100 = 25\% \]

### Final Answer
The profit percentage when selling the tape recorder for Rs. 1000 is **25%**.

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