False weights while claiming cost price — computing hidden gain A dealer claims to sell at cost price but secretly uses a short weight. His gain is 6 18/47 percent. When a customer asks for 1 kg, what weight (in grams) does he actually give?

Introduction / Context:
False-weight problems assume the dealer charges for 1 kg but gives less. Even if the quoted price equals cost price per kg, giving a lower mass produces a percentage gain. We relate percentage gain to the fraction of a kilogram actually delivered.

Given Data / Assumptions:

• Quoted as selling at cost price per kg.
• Actual gain = 6 18/47% = (300/47) %.
• Let w kg be the weight actually delivered instead of 1 kg.

Concept / Approach:
If the dealer charges for 1 kg at cost C per kg, revenue = C. His cost is C × w. Profit fraction on cost = (Revenue − Cost)/Cost = (C − Cw)/(Cw) = (1/w) − 1. Set this equal to the gain expressed as a fraction (not percent).

Step-by-Step Solution:
Gain fraction = (300/47)% / 100 = 3/47.(1/w) − 1 = 3/47 ⇒ 1/w = 1 + 3/47 = 50/47.Therefore w = 47/50 = 0.94 kg = 940 g.

Verification / Alternative check:
With w = 0.94, gain fraction = (1/0.94) − 1 ≈ 0.0638298 = 6.38298% = 300/47%, confirming the statement.

Why Other Options Are Wrong:
953 g, 947 g, 950 g, 960 g do not yield the exact gain percentage when substituted into (1/w) − 1.

Common Pitfalls:
Using gain% directly without converting to a fraction, or mistakenly equating gain% with (1 − w) instead of (1/w − 1).

Final Answer:
940 g