A fruit seller sells mangoes at the rate of Rs. 9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?

Options

A. Rs. 11.81
B. Rs. 12
C. Rs. 12.25
D. Rs. 12.31

Answer

To solve the problem step by step, we will first determine the cost price of the mangoes based on the information provided about the selling price and the loss percentage. Then, we will calculate the selling price required to achieve a profit of 5%.

### Step 1: Determine the Cost Price (CP)

Given:
- Selling Price (SP) = Rs. 9 per kg
- Loss = 20%

To find the cost price when there is a loss, we use the formula:

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

Substituting the values:

\[ 9 = \text{CP} \times \left(1 - \frac{20}{100}\right) \]

This simplifies to:

\[ 9 = \text{CP} \times 0.8 \]

Now, we can solve for CP:

\[ \text{CP} = \frac{9}{0.8} = 11.25 \]

### Step 2: Calculate the Selling Price for a Profit of 5%

To find the selling price that would yield a profit of 5%, we use the formula:

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

Substituting the values:

\[ \text{SP} = 11.25 \times \left(1 + \frac{5}{100}\right) \]

This simplifies to:

\[ \text{SP} = 11.25 \times 1.05 \]

Calculating this gives:

\[ \text{SP} = 11.8125 \]

### Conclusion

Thus, the price per kg at which the fruit seller should sell the mangoes to make a profit of 5% is **Rs. 11.81 (approximately)**.

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