A vendor sells a coconut at Rs 24 and suffers 24% loss. If he wants to make 14% profit, then at what price (in Rs) should he sell?

Options

A. 32
B. 30
C. 36
D. 28

Answer

To solve the problem step by step, we need to determine the cost price (CP) of the coconut first, and then calculate the selling price (SP) required to achieve a 14% profit.

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

Given:
- Selling Price (SP) = Rs 24
- Loss Percentage = 24%

We know that if there is a loss, the Selling Price is given by the formula:
\[ SP = CP \times \left(1 - \frac{Loss \%}{100}\right) \]

Rearranging the formula to find the Cost Price (CP):
\[ CP = \frac{SP}{1 - \frac{Loss \%}{100}} \]

Substituting the values:
\[ CP = \frac{24}{1 - \frac{24}{100}} \]
\[ CP = \frac{24}{1 - 0.24} \]
\[ CP = \frac{24}{0.76} \]
\[ CP = 31.58 \text{ (approximately)} \]

### Step 2: Calculate the Selling Price for 14% Profit

Now, we need to find the new Selling Price (SP) that would give a 14% profit on the Cost Price.

The formula for Selling Price when there is a profit is:
\[ SP = CP \times \left(1 + \frac{Profit \%}{100}\right) \]

Substituting the values:
\[ SP = 31.58 \times \left(1 + \frac{14}{100}\right) \]
\[ SP = 31.58 \times \left(1 + 0.14\right) \]
\[ SP = 31.58 \times 1.14 \]
\[ SP = 36.00 \text{ (approximately)} \]

### Final Answer
The vendor should sell the coconut at Rs 36.00 to achieve a 14% profit.

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