A dishonest shopkeeper claims to sell grocery items at cost price but actually uses a false weight of 900 grams while charging customers for 1 kilogram. Assuming his listed cost price is for 1,000 grams, what is his percentage gain due to using the false weight?

Introduction / Context:
This question involves cheating by using a false weight while claiming to sell at cost price. The shopkeeper pretends to give 1 kilogram but actually delivers only 900 grams. Since customers pay for 1 kilogram but receive less, the shopkeeper earns an effective profit without changing the labelled price. Calculating this gain requires understanding that the cost is for the actual quantity supplied, whereas the revenue is based on the claimed quantity.

Given Data / Assumptions:

• The cost price (CP) is quoted for 1,000 grams (1 kilogram) of grocery.
• The shopkeeper uses a false weight of 900 grams but charges customers for 1 kilogram.
• He sells at the listed cost price per kilogram, so there is no apparent price markup.
• Water or any other adulteration is not mentioned; only weight cheating is considered.
• We must find his percentage gain based purely on short-weighting.

Concept / Approach:
The trick is to assume a convenient cost price for 1 kilogram and then consider how much the shopkeeper pays for 900 grams. Since the selling price is equal to the cost price of 1,000 grams, but he only delivers 900 grams, the difference between revenue and actual cost of 900 grams is the profit. Profit percentage is then calculated as usual: profit% = (profit / cost price of quantity sold) * 100.

Step-by-Step Solution:
Assume cost price of 1 kg of grocery = Rs. 1 (for easy calculation). Therefore, cost price per gram = Rs. 1 / 1,000. Actual quantity given to customer = 900 grams. Cost of 900 grams = 900 * (1 / 1,000) = Rs. 0.90. The shopkeeper charges the customer for 1 kg at cost price, so selling price (SP) = Rs. 1. Profit = SP − CP (for 900 g) = 1 − 0.90 = Rs. 0.10. Profit percentage = (Profit / Cost price of quantity sold) * 100. Profit percentage = (0.10 / 0.90) * 100. 0.10 / 0.90 = 1 / 9 ≈ 0.1111. Therefore, profit percentage ≈ 0.1111 * 100 = 11.11% = 100/9%.

Verification / Alternative check:
We can also assume any other cost price, for example Rs. 90 for 1 kg. Then CP for 900 grams = 0.9 * 90 = Rs. 81. He charges the customer Rs. 90 for this quantity. Profit = 90 − 81 = Rs. 9. Profit percentage = (9 / 81) * 100 = (1 / 9) * 100 = 11.11%, again confirming 100/9% as the exact fractional form.

Why Other Options Are Wrong:
91/9% and 95/9%: These correspond to much larger profit percentages and arise from misinterpreting the cost base or using the wrong reference quantity.
100/11%: This is a different fraction and does not match the computed ratio of 1/9.
11.11%: While numerically equivalent to 100/9%, the answer options are expected in fractional form, and 100/9% is the more precise representation given in the choices.

Common Pitfalls:
Some students incorrectly treat the cost price as that of 900 grams instead of 1,000 grams, or they apply profit percentage on selling price instead of cost price. Another common mistake is forgetting to convert grams to kilograms consistently or using 100 grams as a base instead of 1,000 grams, which can change the numbers. Always choose a simple assumption (like CP = Rs. 1 for 1 kg) and then compute the cost of the actual quantity delivered.

Final Answer:
The dishonest shopkeeper's gain due to using a false 900 gram weight is 100/9%, which is approximately 11.11%.