On selling rice for Rs 45 per kg, a shopkeeper bears loss of 20%. To earn a profit of 20%, the selling price should be
A. Rs 67.50
B. Rs 65
C. Rs 70
D. Rs 60

Options

A. B
B. D
C. A
D. C

Answer

To solve the problem step by step, we will first determine the cost price of the rice based on the given selling price and loss percentage. Then, we will calculate the new selling price required to achieve a profit of 20%.

### Step 1: Determine the Cost Price (CP)
Given:
- Selling Price (SP) = Rs 45 per kg
- Loss Percentage = 20%

To find the Cost Price (CP), we can use the formula:
\[ CP = \frac{SP \times 100}{100 - \text{Loss Percentage}} \]

Substituting the values:
\[ CP = \frac{45 \times 100}{100 - 20} = \frac{4500}{80} = 56.25 \]

### Step 2: Calculate the Selling Price for a 20% Profit
Now that we have the Cost Price, we need to find the new Selling Price (SP') that would give a profit of 20%.

The formula for Selling Price when profit percentage is given is:
\[ SP' = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]

Substituting the values:
\[ SP' = 56.25 \times \left(1 + \frac{20}{100}\right) = 56.25 \times 1.2 = 67.50 \]

### Conclusion
The Selling Price required to earn a profit of 20% is Rs 67.50.

### Final Answer
The correct option is **A. Rs 67.50**.

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