A shopkeeper states that each item is sold at a profit of 2%, but the “1 kg” weight he uses actually weighs only 960 g. What is his true profit or loss percentage?

The correct option is 6.25% profit.

Step-by-step Explanation:

Let us assume the cost price (CP) of 1 gram of goods is 1 unit of money (e.g., ₹1).

Step 1: Calculate the Stated Selling Price (SP)
The shopkeeper claims to sell 1 kg (1000 grams) at a profit of 2%.
Cost price of 1000 grams = 1000 units.
Stated Selling Price (SP) for 1 kg = 1000 + 2% of 1000

$\text{Stated SP}=1000+(\frac{2}{100}\times 1000)=1020\text{units}$

So, the customer pays 1020 units believing they are purchasing 1000 grams.

Step 2: Calculate the Actual Cost Price to the Shopkeeper
The shopkeeper uses a false weight that actually weighs only 960 grams instead of 1000 grams.
Therefore, the shopkeeper only delivers 960 grams of goods for the 1020 units received.
Actual Cost Price (CP) of 960 grams to the shopkeeper = 960 units.

Step 3: Calculate the True Profit
True Profit = Stated SP - Actual CP

$\text{Profit}=1020-960=60\text{units}$

Step 4: Calculate the True Profit Percentage
The true profit percentage is based on the actual cost incurred by the shopkeeper for the goods supplied:

$\text{True Profit \%}=\frac{\text{Profit}}{\text{Actual CP}}\times 100$

$\text{True Profit \%}=\frac{60}{960}\times 100$

$\text{True Profit \%}=\frac{1}{16}\times 100=6.25\%$

Since the calculated percentage is positive, the shopkeeper makes a true profit of 6.25%.