M/s Mehta Fruits and Vegetables sell apples at the rate of Rs.9 per kg and therby lost `20%`. At what price(per kg), they should have sold them to make a profit of `5%`?

Options

A. Rs11.32
B. Rs11
C. Rs12
D. Rs11.81

Answer

To solve the problem step by step, we will find the cost price of the apples first and then determine the selling price required to achieve a profit of 5%.

### Step 1: Find the Cost Price (CP) of Apples
Given:
- Selling Price (SP) = Rs. 9 per kg
- Loss Percentage = 20%

The formula to find the cost price when there is a loss is:
\[ SP = (1 - \text{Loss Percentage}) \times CP \]

Substituting the values:
\[ 9 = (1 - 0.20) \times CP \]
\[ 9 = 0.80 \times CP \]

Now, we can solve for CP:
\[ CP = \frac{9}{0.80} \]
\[ CP = \frac{9 \times 100}{80} \]
\[ CP = \frac{900}{80} \]
\[ CP = 11.25 \text{ Rs. per kg} \]

### Step 2: Find the Selling Price (SP) for a 5% Profit
To find the selling price for a profit of 5%, we use the formula:
\[ SP = (1 + \text{Profit Percentage}) \times CP \]

Substituting the values:
\[ SP = (1 + 0.05) \times 11.25 \]
\[ SP = 1.05 \times 11.25 \]

Now, we can calculate the SP:
\[ SP = 11.8125 \text{ Rs. per kg} \]

### Final Answer
Thus, the selling price per kg to achieve a profit of 5% is approximately Rs. 11.81.

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