A retailer cheats both the wholesaler and his customers by 10% using a faulty balance: he weighs 10% more while buying and 10% less while selling, and sells at the listed cost price. Find his net profit percentage.

Introduction:
The retailer gains twice: he receives extra quantity when purchasing, and he delivers less when selling. Even if he “sells at cost price” per kg (nominal), the net effect is a profit when measured against the true cost of goods delivered. We quantify the combined effect.

Given Data / Assumptions:

• Buys: for each 1 kg paid, receives 1.1 kg (10% extra)
• Sells: for each 1 kg billed, delivers 0.9 kg (10% short)
• Nominal selling price per kg equals listed cost price per kg = C

Concept / Approach:
For one “kg sale”: revenue = C. True cost of the 0.9 kg delivered equals 0.9 times the true cost per kg the retailer effectively paid. Since he got 1.1 kg for the price of 1 kg, his true cost per kg is C/1.1. Compute profit% on cost of goods delivered.

Step-by-Step Solution:
Cost per true kg to retailer = C / 1.1Cost for 0.9 kg delivered = (C / 1.1) * 0.9 = 0.81818... * CRevenue per sale = CProfit = C − 0.81818... C = 0.18181... CProfit% = 0.18181... / 0.81818... * 100 = 22.222...% = 22 2/9%

Verification / Alternative check:
On 11 kg bought (paying 10 kg): he sells in “1 kg” lots, each delivering 0.9 kg; 11 kg supports 12.22... “kg” bills—consistent with a 22.22...% edge overall.

Why Other Options Are Wrong:
20%, 21%: Understate the compounding of the two 10% cheats.22 2/2%: Not a standard fraction here; correct exact value is 22 2/9%.

Common Pitfalls:
Computing profit% on selling price; ignoring that cost per true kg is reduced by the 10% extra received at purchase.

Final Answer:
22 2/9%