By selling a pen for Rs 105 there is a loss of 30%. At what price (in Rs) the pen must be sold in order to gain 30%?

Options

A. 215
B. 165
C. 195
D. 200

Answer

To solve the problem step by step, we need to find the cost price (CP) of the pen first, and then determine the selling price (SP) required to achieve a 30% profit.

### Step 1: Determine the Cost Price (CP)
Given that selling the pen for Rs. 105 results in a loss of 30%, we can use the formula for loss:

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

Since there is a loss of 30%, we can express the selling price in terms of the cost price:

\[ \text{SP} = \text{CP} - 0.30 \times \text{CP} = 0.70 \times \text{CP} \]

Given that SP = Rs. 105, we can set up the equation:

\[ 0.70 \times \text{CP} = 105 \]

### Step 2: Solve for CP
To find the cost price (CP), we can rearrange the equation:

\[ \text{CP} = \frac{105}{0.70} \]

Calculating this gives:

\[ \text{CP} = 150 \]

### Step 3: Calculate the Selling Price for a 30% Gain
Now that we have the cost price, we can find the selling price required for a 30% gain. The formula for gain is:

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

For a 30% gain, the selling price can be expressed as:

\[ \text{SP} = \text{CP} + 0.30 \times \text{CP} = 1.30 \times \text{CP} \]

Substituting the value of CP we found:

\[ \text{SP} = 1.30 \times 150 \]

Calculating this gives:

\[ \text{SP} = 195 \]

### Conclusion
To gain a 30% profit, the pen must be sold for Rs. 195.

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