A dealer earned a profit of 5% by selling a radio for `₹714`. Find the cost price of the radio.

Options

A. `₹580`
B. `₹780`
C. `₹680`
D. `₹980`

Answer

To find the cost price of the radio when the dealer earned a profit of 5% by selling it for ₹714, we can follow these steps:

### Step 1: Understand the relationship between Selling Price, Cost Price, and Profit
The relationship can be expressed as:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Since profit is calculated as a percentage of the cost price, we can also express it as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times \text{Cost Price (CP)} \]

### Step 2: Set up the equation
Given that the selling price (SP) is ₹714 and the profit percentage is 5%, we can write:
\[ 714 = \text{CP} + \left(\frac{5}{100} \times \text{CP}\right) \]

### Step 3: Simplify the equation
We can express the profit in terms of CP:
\[ 714 = \text{CP} + 0.05 \times \text{CP} \]
\[ 714 = \text{CP} (1 + 0.05) \]
\[ 714 = \text{CP} \times 1.05 \]

### Step 4: Solve for Cost Price (CP)
To find the cost price, we can rearrange the equation:
\[ \text{CP} = \frac{714}{1.05} \]

### Step 5: Calculate the value
Now, we can calculate the cost price:
\[ \text{CP} = \frac{714}{1.05} = 680 \]

### Conclusion
The cost price of the radio is ₹680.

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