A trader sells at k% above cost but delivers only 880 g instead of 1 kg. If his overall profit is 25%, find k.

Introduction:
A short-weight trick increases effective price per true kilogram. Combined with a markup k% on cost, the overall profit becomes 25%. We compute k so that revenue on a “1 kg” sale compared to the true cost of 0.88 kg delivered yields a 25% margin.

Given Data / Assumptions:

• True cost per kg = C
• Delivered per “1 kg” bill = 0.88 kg
• Nominal SP per “1 kg” = C * (1 + k)
• Target overall profit = 25%

Concept / Approach:
Profit% on cost of goods delivered = [(Revenue − Cost)/Cost] * 100 with Cost = 0.88C and Revenue = C(1 + k). Set it equal to 25% and solve for k.

Step-by-Step Solution:
[(C(1 + k) − 0.88C) / (0.88C)] = 0.25(k + 0.12)/0.88 = 0.25 ⇒ k + 0.12 = 0.22 ⇒ k = 0.10Therefore k = 10%

Verification / Alternative check:
At k = 10%, revenue = 1.10C; cost for 0.88 kg = 0.88C; profit% = (0.22C)/(0.88C) = 25%.

Why Other Options Are Wrong:
8.33%/8.25%/12.5% give overall margins different from 25% with 0.88 kg delivered.

Common Pitfalls:
Computing profit on SP; forgetting to account for the reduced quantity delivered.

Final Answer:
10%