Profit and Loss – Short weight deception at “cost price”: A dealer claims to sell at cost price but uses a 900 g weight as if it were 1 kg. What is his actual gain percentage?

Introduction / Context:
Using a short weight increases the effective price per kilogram, creating a hidden gain even if the stated price equals the cost price per kilogram.

Given Data / Assumptions:

• Claimed unit: 1 kg
• Actual delivered: 900 g
• Quoted price equals cost price per 1 kg

Concept / Approach:
If customer pays for 1 kg but receives only 0.9 kg, the dealer collects the price of 1 kg while parting with 0.9 kg that costs him less. Gain% is computed on dealer’s cost for 0.9 kg.

Step-by-Step Solution:
Let cost price per kg = Rs 100 (any convenient number)Dealer sells “1 kg” at Rs 100 but gives 0.9 kg whose cost = 0.9 * 100 = Rs 90Gain = 100 - 90 = Rs 10Gain% = 10 / 90 * 100 = 11.111...% = 11 1/9%

Verification / Alternative check:
Formula: gain% = (1000 - 900) / 900 * 100 = 11.111...%

Why Other Options Are Wrong:
11%, 10%, and 9% are approximations that do not match the exact 11 1/9%. 12.5% is too high.

Common Pitfalls:
Using 1000 as the denominator or computing profit on SP rather than CP.

Final Answer:
11 1/9%