During a sale 50% of the goods are sold at 19% profit, 20% of the remaining goods are sold at 40% profit and the still remaining goods are sold at a loss of 25%. If there is an overall profit of x%, then what is the value of x?

The correct option is 3.5.

To find the value of $x$ (the overall profit percentage), let us assume the total quantity of goods is 100 units, and the cost price (CP) of each unit is 1. Therefore, the total cost price of all the goods is 100.

Now, let us calculate the profit or loss from each transaction step-by-step:
1. First part of the sale:
50% of the total goods are sold at a 19% profit.
Quantity of goods sold = 50% of 100 = 50 units.
Cost Price of these goods = 50.
Profit earned = 19% of 50 = $\frac{19}{100}\times 50=9.5$.

2. Second part of the sale:
Remaining goods = 100 - 50 = 50 units.
20% of these remaining goods are sold at a 40% profit.
Quantity of goods sold = 20% of 50 = 10 units.
Cost Price of these goods = 10.
Profit earned = 40% of 10 = $\frac{40}{100}\times 10=4$.

3. Third part of the sale:
Still remaining goods = 50 - 10 = 40 units.
These goods are sold at a loss of 25%.
Cost Price of these goods = 40.
Loss incurred = 25% of 40 = $\frac{25}{100}\times 40=10$ (which represents a negative profit of -10).

Next, we calculate the total net profit by combining the results of all three parts:
Total Net Profit = Profit from part 1 + Profit from part 2 - Loss from part 3
Total Net Profit = 9.5 + 4 - 10 = 3.5.

Finally, we find the overall profit percentage ($x$):
$x=\left(\frac{\text{Total Net Profit}}{\text{Total Cost Price}}\right)\times 100$
$x=\left(\frac{3.5}{100}\right)\times 100=3.5$.

Thus, the value of $x$ is 3.5, representing an overall profit of 3.5%.