A trader’s balance weighs 10% less than true weight. He still wants an overall profit of 20%. What markup on cost price is required (no discount assumed)?

Introduction:
Under-weighing means that when the trader bills 1 kg, the customer actually receives only 0.9 kg. If the trader also marks up his price, we can choose the markup so that the net profit on the cost of goods delivered is exactly 20%.

Given Data / Assumptions:

• True cost per kg = C
• Actual quantity delivered for a “1 kg” sale = 0.9 kg
• Required overall profit = 20%
• Let markup on cost = m (so SP for 1 “kg” = C * (1 + m))

Concept / Approach:
Profit% on cost of goods delivered = [(Revenue − Cost)/Cost] * 100. Here, Cost = 0.9 * C and Revenue = C * (1 + m). Set this profit equal to 20% and solve for m.

Step-by-Step Solution:
Profit% = [(C(1 + m) − 0.9C) / (0.9C)] * 100 = [(0.1 + m)/0.9] * 100Set [(0.1 + m)/0.9] = 0.20 ⇒ 0.1 + m = 0.18 ⇒ m = 0.08Required markup = 8%

Verification / Alternative check:
Revenue at m = 8%: 1.08C; cost of 0.9 kg = 0.9C; profit% = 0.18C / 0.9C = 20%.

Why Other Options Are Wrong:
16.66% or 25% overshoot; 40% is excessive for a 10% under-weight scenario at 20% target profit.

Common Pitfalls:
Calculating profit on selling price base; forgetting that the under-weighing already contributes part of the margin (0.1/0.9 ≈ 11.11%).

Final Answer:
8%