A vendor sells a suitcase for Rs. 1600 and makes a loss of 20%. At what price should the suitcase be sold to earn a profit of 20%?

The correct option is Rs. 2400.

To determine the price at which the vendor should sell the suitcase to earn a 20% profit, we must first find the original Cost Price (CP) of the suitcase.

Step 1: Find the Cost Price (CP) of the suitcase
When an item is sold at a loss, the Selling Price (SP) is related to the Cost Price (CP) by the following formula:

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

Given parameters:
Initial Selling Price (SP) = Rs. 1600
Loss Percentage = 20%

Substituting the given values into the formula:

$1600=\text{CP}\times \left(1-\frac{20}{100}\right)$

$1600=\text{CP}\times \left(1-0.20\right)$

$1600=\text{CP}\times 0.80$

Solving for CP:

$\text{CP}=\frac{1600}{0.80}=2000$

The Cost Price of the suitcase is Rs. 2000.

Step 2: Calculate the Selling Price for a 20% Profit
To earn a profit of 20%, we calculate the new Selling Price using the profit formula:

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

Substitute CP = Rs. 2000 and Profit Percentage = 20% into the equation:

$\text{New SP}=2000\times \left(1+\frac{20}{100}\right)$

$\text{New SP}=2000\times 1.20$

$\text{New SP}=2400$

Therefore, the suitcase should be sold for Rs. 2400 to earn a profit of 20%.