Dishonest Dealer & False Weights

🎯 Learning Objective

Compute the real gain per cent of a dealer who sells at cost price but uses false weights.

💡 Concept

• A dishonest dealer claims to sell at CP but gives less quantity using a false weight
• Error = claimed weight − actual weight given
• Gain% = [Error / (True weight − Error)] × 100
• Base is what he ACTUALLY gives, not what he claims
• If he also marks up or gives discount, combine the effects with multiplying factors

🧮 Key Formulas

Gain% = Error × 100 / (True weight − Error)

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Error = weight the dealer keeps back

✏️ Easy Example

Q. A shopkeeper sells at cost price but uses an 800 g weight in place of 1 kg. Find his gain per cent.

1. Error = 1000 − 800 = 200 g
2. Gain% = 200 × 100 / 800

Answer: 25%

🇮🇳 Real-Life Example

The mandi scene where a 1 kg 'stone' actually weighs 900 g — the seller pockets 11.11% extra without changing a single price board.

📝 Exam-Level Example

Q. A dealer sells goods at cost price but uses a 900 g weight for 1 kg. Find his gain per cent.

1. Error = 1000 − 900 = 100 g
2. Gain% = 100 × 100 / 900
3. = 100/9

Answer: 11.11% (11 1/9%)

📝 Exam-Level Example

Q. A dishonest dealer professes to sell at a 10% loss but gives only 750 g for 1 kg. Find his actual gain per cent.

1. Take CP = ₹1 per gram
2. He collects 90% of 1000 = ₹900
3. Goods actually given cost ₹750
4. Gain% = (150/750) × 100

Answer: 20% gain

🪄 Memory Trick

Assume CP = ₹1 per gram. Money received minus cost of goods actually given — the gap is pure profit.

⚠️ Common Mistakes

• ❌ Dividing the error by the true weight (1000) instead of the actual weight given
• ❌ Treating a professed loss as a real loss without checking the false weight
• ❌ Mixing grams and kilograms in the same equation

🏆 Exam Tips

• ✅ Memorise the common answers: 900 g → 11.11%, 800 g → 25%, 750 g → 33.33%
• ✅ The ₹1-per-gram assumption works in every dishonest-dealer question

📌 Summary

• False weight → gain even when selling at CP
• Gain% = Error/(True − Error) × 100
• Base = quantity actually given
• Combined tricks → fall back to ₹1 per gram