A dishonest seller gives only 840 grams of goods to customers while charging them for 1 kilogram. He also claims that he is selling at a loss of 4% on cost price. What is his actual percentage profit or loss?

Introduction / Context:
This question combines two core ideas from profit and loss: cheating in weights and percentage loss on cost price. Many shopkeepers in aptitude problems use less quantity than they claim in order to gain extra profit even while pretending to give a discount or incur a loss. You must track both the quantity sold and the quoted loss percentage to find the true profit or loss.

Given Data / Assumptions:

• Seller charges for 1 kg but actually gives only 840 g.
• He claims to sell at 4% loss on cost price.
• We assume cost price is per kilogram of goods.
• We need to calculate the true percentage profit or loss.

Concept / Approach:
The trick is to compare what the seller receives (selling price for 1 kg) with what it actually costs him (cost of 840 g). First, assume a convenient cost price for 1 kg, say Rs 100. Then use the claimed 4% loss to find the selling price for 1 kg. Since he really gives only 840 g for this price, his effective cost for that quantity is less, leading to profit. Finally compute actual profit% on the cost of 840 g.

Step-by-Step Solution:
Step 1: Assume cost price of 1 kg = Rs 100.Step 2: With a 4% loss, selling price for 1 kg (as claimed) SP = 0.96 * 100 = Rs 96.Step 3: In reality, when he charges Rs 96, he gives only 840 g. So actual cost to him for 840 g = (840 / 1000) * 100 = Rs 84.Step 4: Actual profit for 840 g = SP - actual CP = 96 - 84 = Rs 12.Step 5: Actual profit% = (12 / 84) * 100 = 14.2857% ≈ 14.28% profit.

Verification / Alternative check:
You may choose any other convenient cost price, such as Rs 50 per kg. Then SP = 0.96 * 50 = Rs 48 and cost of 840 g = 0.84 * 50 = Rs 42. Profit = 48 - 42 = Rs 6, and profit% = (6 / 42) * 100 = 14.2857%, giving the same result. This proves that the percentage profit is independent of the assumed base cost price.

Why Other Options Are Wrong:
24.18 % profit or loss and 14.28 % loss result from wrongly treating the loss as genuine and ignoring the cheating in weight, or from using 1 kg repeatedly without scaling down to 840 g. The sign must be profit, not loss, because the seller receives more money than the true cost of the goods he actually hands over.

Common Pitfalls:
Many learners simply apply 4% loss on cost and stop, taking it as the final answer. Others compute profit% using 96 and 100 directly without adjusting for the short weight. Always remember that if the quantity given to the customer is less than what is charged for, you must first find the cost of the smaller quantity and then compare with the selling price. This is the only way to get the true profit or loss percentage.

Final Answer:
The seller is actually making a profit of about 14.28 % profit on his goods.