On selling an article for Rs 455, a shopkeeper losses 30%. For how much (in Rs) he should sell the article in order to earn a profit of 30%?

Options

A. 750
B. 245
C. 845
D. 680

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article based on the selling price (SP) and the loss percentage. Then, we will calculate the selling price required to achieve a profit of 30%.

### Step 1: Calculate the Cost Price (CP)
Given:
- Selling Price (SP) = Rs 455
- Loss Percentage = 30%

When there is a loss of 30%, it means the selling price is 70% of the cost price. Therefore, we can set up the equation:

\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]

Substituting the known values:

\[ 455 = CP \times \left(1 - \frac{30}{100}\right) \]

This simplifies to:

\[ 455 = CP \times 0.7 \]

Now, we can solve for CP:

\[ CP = \frac{455}{0.7} \]

Calculating this gives:

\[ CP = 650 \]

### Step 2: Calculate the Selling Price for a Profit of 30%
To find the selling price that would yield a profit of 30%, we use the formula:

\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]

Substituting the cost price and profit percentage:

\[ SP = 650 \times \left(1 + \frac{30}{100}\right) \]

This simplifies to:

\[ SP = 650 \times 1.3 \]

Calculating this gives:

\[ SP = 845 \]

### Final Answer
The shopkeeper should sell the article for Rs 845 to earn a profit of 30%.

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