A dishonest shopkeeper claims to sell goods at cost price but uses a false weight of 950 grams instead of a true kilogram (1000 grams). What is his gain percentage in this situation?

Introduction / Context:
This is a typical question on cheating in weights and measures. The shopkeeper pretends to sell one kilogram but actually gives only 950 grams while charging the full price of 1 kilogram. Such questions test understanding of effective selling price and cost price per true unit and how this creates a hidden profit percentage even when the claimed selling price matches the stated cost price.

Given Data / Assumptions:

• Shopkeeper claims to sell 1 kilogram of goods at cost price.
• Actual quantity given to the customer is 950 grams.
• Customer pays the price meant for 1000 grams.
• Let the cost price of 1 kilogram be C rupees.
• We need the gain percentage based on true cost.

Concept / Approach:
If 1 kilogram costs C rupees, then the cost of 950 grams is proportional. The dishonest shopkeeper collects C rupees from the customer but spends only the cost of 950 grams. The difference between these two amounts is the hidden profit. Profit percentage is computed as (Profit / Cost of goods actually given) * 100. The key is to treat 950 grams as the real cost basis, since that is the amount of goods actually delivered.

Step-by-Step Solution:
Step 1: Let cost price of 1000 grams (1 kilogram) be C rupees.Step 2: Cost price of 1 gram = C / 1000.Step 3: Cost price of 950 grams = 950 * (C / 1000) = 0.95C.Step 4: The shopkeeper sells 950 grams but charges for 1000 grams at cost price, so selling price SP = C rupees.Step 5: Profit = SP - CP of goods actually sold = C - 0.95C = 0.05C.Step 6: Profit percentage = (Profit / CP) * 100 = (0.05C / 0.95C) * 100.Step 7: Simplify ratio: 0.05 / 0.95 = 5 / 95 = 1 / 19.Step 8: Profit percentage = (1 / 19) * 100 = 100 / 19%.

Verification / Alternative check:
We can use a numerical example. Assume C = Rs 100 for 1 kilogram. Then the cost of 950 grams is 0.95 * 100 = Rs 95. The shopkeeper collects Rs 100 from the customer. Profit = 100 - 95 = Rs 5. Profit percentage = 5 / 95 * 100 ≈ 5.263%, which is exactly 100 / 19%. This numerical confirmation verifies the algebraic steps and shows that the answer is precise.

Why Other Options Are Wrong:
Option A (100/23%), option C (100/17%) and option D (100/21%) are all close looking fractions but none match the ratio 5 / 95. Only 100 / 19 corresponds to the exact fraction (1/19) * 100 obtained from the correct computation. The other denominators represent different hidden profit margins that would arise from different false weights, not the given 950 grams case.

Common Pitfalls:
A common mistake is to compute profit percentage with base 1000 grams instead of the 950 grams actually supplied, which leads to a smaller and incorrect percentage. Others incorrectly assume that the profit is exactly 5% without accounting for the smaller base. Always remember that percentage profit is calculated on the cost of goods actually given away, which in cheating questions is usually lower than the claimed quantity.

Final Answer:
The dishonest shopkeeper gains 100/19% profit by using the 950 gram weight instead of a true kilogram.