Calculating the original selling price
To find out the profit/loss percentage of an item, we need to first calculate the original selling price of the item. Here, we know that the trader gained 40% by selling the item. This means that the selling price is 140% of the original price.

Using the formula
If we let the original selling price be x, then we can use the formula:
Selling price = Original selling price + Profit
140% of x = x + 40% of x
1.4x = x + 0.4x
1.4x = 1.4x
Therefore, the original selling price is x.

Calculating the new selling price
If the item is sold for half the price, the selling price will be 50% of the original selling price.

Using the formula
Let the new selling price be y. Then we can use the formula:
50% of x = y
0.5x = y

Calculating the profit/loss percentage
To calculate the profit/loss percentage, we need to compare the original selling price with the new selling price.

Using the formula
Profit/loss percentage = (New selling price - Original selling price) / Original selling price x 100%
Profit/loss percentage = (y - x) / x x 100%
Profit/loss percentage = ((0.5x) - x) / x x 100%
Profit/loss percentage = -0.5 x 100%
Profit/loss percentage = -50%

Explaining the result
The negative sign in the profit/loss percentage indicates a loss. The item is being sold for half the price, which means that the new selling price is 50% of the original selling price. This is a 50% decrease in the selling price, which results in a 50% loss for the trader.

30 percent loss