A radio is sold for Rs. 880 at a profit of 10%. What would have been the gain or loss percent, had it been sold for Rs. 780 ?

Options

A. (a) 2½ %
B. (b) 3¼ %
C. (c) 3½ %
D. (d) 5¾ %

Answer

To solve the problem step by step, we need to find the cost price (CP) of the radio first and then determine the loss percentage when it is sold for Rs. 780.

### Step 1: Find the Cost Price (CP)
Given:
- Selling Price (SP) = Rs. 880
- Profit Percentage = 10%

We can use the formula for Cost Price based on Selling Price and Profit Percentage:

\[ CP = \frac{SP \times 100}{100 + \text{Profit Percentage}} \]

Substituting the values:

\[ CP = \frac{880 \times 100}{100 + 10} = \frac{88000}{110} \]

Calculating the above:

\[ CP = 800 \]

### Step 2: Determine the Selling Price for the second scenario
The new Selling Price (SP) is Rs. 780.

### Step 3: Identify if there is a loss
Since the new SP (Rs. 780) is less than the CP (Rs. 800), there is a loss.

### Step 4: Calculate the Loss
Loss can be calculated as:

\[ \text{Loss} = CP - SP = 800 - 780 = 20 \]

### Step 5: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:

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

Substituting the values:

\[ \text{Loss Percentage} = \left(\frac{20}{800}\right) \times 100 \]

Calculating the above:

\[ \text{Loss Percentage} = \frac{20 \times 100}{800} = \frac{2000}{800} = 2.5\% \]

### Final Answer
The loss percentage when the radio is sold for Rs. 780 is **2.5%**.

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