This question asks us to determine the new selling price for an orange if the vendor wants to achieve a 78% profit, given that the current selling price of ₹44 results in a 78% loss.

Calculating the Cost Price (CP) of the Orange

First, we need to find the original cost price (CP) of the orange. The vendor sells the orange for ₹44, incurring a loss of 78%. This means the selling price (SP1) represents the remaining percentage of the cost price after the loss.

• Loss percentage = $78\%$
• The selling price is $(100 - 78)\% = 22\%$ of the cost price.
• Current Selling Price (SP1) = $₹44$

We can set up the equation:

SP1 = CP $\times$ $\frac{100 - \text{Loss}\%}{100}$

Substituting the values:

$₹44 = \text{CP} \times \frac{100 - 78}{100}$

$₹44 = \text{CP} \times \frac{22}{100}$

Now, we solve for CP:

$\text{CP} = \frac{₹44 \times 100}{22}$

$\text{CP} = ₹2 \times 100$

$\text{CP} = ₹200$

So, the cost price of each orange is ₹200.

Calculating the New Selling Price (SP2) for a 78% Profit

Next, we need to calculate the selling price (SP2) required to make a profit of 78%. A profit of 78% means the selling price will be the cost price plus 78% of the cost price.

• Cost Price (CP) = $₹200$
• Desired Profit percentage = $78\%$

The formula for the new selling price is:

SP2 = CP $\times$ $\frac{100 + \text{Profit}\%}{100}$

Substituting the values:

$\text{SP2} = ₹200 \times \frac{100 + 78}{100}$

$\text{SP2} = ₹200 \times \frac{178}{100}$

$\text{SP2} = ₹2 \times 178$

$\text{SP2} = ₹356$

Therefore, the vendor should sell each orange for ₹356 to make a profit of 78%.