A trader uses a faulty balance that shows 1250 g as 1 kg, and he also marks up his cost price by 20%. Find his overall profit percentage.

Introduction:
Here, the trader benefits twice: by marking up the price and by under-delivering weight due to a miscalibrated balance. We compute the compound effect relative to the true cost of goods delivered.

Given Data / Assumptions:

• Scale shows 1 kg when actual is 0.8 kg (since 1.25 kg shows as 1 kg, the factor is actual = shown / 1.25)
• Markup on cost price = 20%
• Let true cost per kg = C rupees

Concept / Approach:
For one “kg sale” (based on the faulty balance): revenue = 1.20 * C; actual quantity delivered = 0.8 kg; cost of delivered goods = 0.8 * C. Profit% is computed on the cost of goods delivered.

Step-by-Step Solution:
Revenue per sale = 1.2 * CCost per sale = 0.8 * CProfit = 1.2C − 0.8C = 0.4CProfit% = (0.4C)/(0.8C) * 100 = 50%

Verification / Alternative check:
Even without markup, under-delivery would create gain; with an added 20% markup, profit reaches exactly 50% under these parameters.

Why Other Options Are Wrong:
5%, 30%, 45%: Do not reflect the combined effect of 20% markup and giving only 0.8 kg.

Common Pitfalls:
Interpreting “shows 1250 g as 1 kg” backwards; computing profit on selling price instead of cost base of goods delivered.

Final Answer:
50 %