A Shop owner gives a discount of 10% on the marked price of a radio, hut in the bargain makes a profit of 10%. If the marked price is 330%. The cost price in rupees -

Options

A. Rs 297
B. Rs 300
C. Rs 315
D. Rs 270

Answer

To find the cost price of the radio, we can follow these steps:

### Step 1: Identify the Marked Price
The marked price (MP) of the radio is given as Rs. 330.

### Step 2: Calculate the Selling Price
The shop owner gives a discount of 10% on the marked price. Therefore, the selling price (SP) can be calculated as follows:

\[ \text{Discount} = 10\% \text{ of } \text{MP} = \frac{10}{100} \times 330 = 33 \]

Now, subtract the discount from the marked price to find the selling price:

\[ \text{SP} = \text{MP} - \text{Discount} = 330 - 33 = 297 \]

### Step 3: Calculate the Cost Price
The shop owner makes a profit of 10% on the cost price (CP). We know that:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Since the profit is 10% of the cost price, we can express it as:

\[ \text{Profit} = 10\% \text{ of } \text{CP} = \frac{10}{100} \times \text{CP} = \frac{1}{10} \times \text{CP} \]

Thus, we can rewrite the selling price equation as:

\[ \text{SP} = \text{CP} + \frac{1}{10} \times \text{CP} = \frac{10}{10} \text{CP} + \frac{1}{10} \text{CP} = \frac{11}{10} \text{CP} \]

Now, we can rearrange this to find the cost price:

\[ \text{CP} = \frac{10}{11} \times \text{SP} \]

### Step 4: Substitute the Selling Price
Now substitute the selling price we calculated earlier:

\[ \text{CP} = \frac{10}{11} \times 297 \]

Calculating this gives:

\[ \text{CP} = \frac{2970}{11} = 270 \]

### Conclusion
The cost price of the radio is Rs. 270.

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