A dishonest dealer claims to sell at cost price but uses a false weight of 900 g as “1 kg”. What is his gain percentage on the true cost of goods delivered?

Introduction / Context:
Short-weight frauds create profit even when the dealer “sells at cost price.” The trick is that the customer is charged for 1 kg but actually receives less. We compare revenue for the billed 1 kg with the true cost of the quantity actually delivered.

Given Data / Assumptions:

• Dealer bills 1 kg at cost price per kg = C rupees.
• Actual quantity delivered = 0.9 kg (900 g).
• Cost base for profit% is the cost of goods delivered.

Concept / Approach:
Revenue per “1 kg” bill = C. Cost of delivered goods = 0.9 * C. Profit = C − 0.9C = 0.1C. Profit% on cost = (0.1C)/(0.9C) * 100 = 11.111...%.

Step-by-Step Solution:
Revenue = CCost (0.9 kg) = 0.9CProfit = 0.1CProfit% = (0.1/0.9) * 100 = 11.111...% = 11 1/9 %

Verification / Alternative check:
On 9 kg actually supplied (billed as 10 kg), total billed amount = 10C; cost = 9C; profit = C; profit% = C/9C = 11.11%.

Why Other Options Are Wrong:
10% and 11% are approximations that underestimate; 12 1/2% is too high.

Common Pitfalls:
Computing profit% on selling price; forgetting that the base should be cost of quantity actually delivered.

Final Answer:
11 1/9 %