Profit and Loss – Dual cheating: 8% while buying and 8% while selling: A trader cheats to the extent of 8% when buying (gets extra goods) and again cheats 8% when selling (gives less goods). What is his overall percentage gain?

Introduction / Context:
This scenario involves quantity-based cheating on both sides of the transaction. When buying, getting 8% extra reduces cost per true unit. When selling, giving 8% less increases revenue per true unit. The total effect is multiplicative on a per-true-unit basis.

Given Data / Assumptions:

• Buys: receives 1.08 true units for the cost of 1 unit
• Sells: delivers only 0.92 true unit for the price of 1 unit

Concept / Approach:
Cost per true unit = 1 / 1.08 (in “money per true unit”). Revenue per true unit = 1 / 0.92 (in “money per true unit”). Overall multiplier = (1 / 0.92) / (1 / 1.08) = 1.08 / 0.92.

Step-by-Step Solution:
Overall factor = 1.08 / 0.92 ≈ 1.173913...Overall gain% = (1.173913... − 1) * 100 ≈ 17.39%

Verification / Alternative check:
Using small numbers: suppose cost for “1 money unit” of labeled goods. He obtains 1.08 true units; selling 0.92 true unit yields 1 money unit; scaling to 1 true unit returns about 1.1739 money units.

Why Other Options Are Wrong:
16.0% and 16.64% understate the multiplicative effect; 15.48% is even lower. “None” is false because 17.39% is correct.

Common Pitfalls:
Adding 8% and 8% to get 16% instead of multiplying the factors 1.08 and 1 / 0.92.

Final Answer:
17.39%