A retailer cheats both wholesaler and customer by receiving 19% extra quantity from the wholesaler and delivering 15% less quantity to the customer while charging the cost price; what is his effective profit percentage?

Introduction / Context:
This question is about dishonest trading practices, where a retailer manipulates quantities while keeping the displayed price unchanged. He receives more goods from the wholesaler than he pays for and gives less to the customer than what he charges for. These tricks create a hidden profit. The task is to compute the effective profit percentage that arises purely from these quantity manipulations when the nominal selling price equals the cost price per unit.

Given Data / Assumptions:

• The retailer pays the wholesaler for a nominal quantity but actually receives 19% more quantity.
• He sells to customers while giving 15% less quantity than what he charges for.
• He charges customers at the same nominal rate as his cost price per unit.
• No additional overheads or taxes are mentioned.
• We must find the net profit percentage based only on the discrepancy between actual and nominal quantities.

Concept / Approach:
Assume a simple base cost price per unit, for example Rs. 1, and a nominal quantity such as 100 units for which the retailer settles accounts. He pays the wholesaler for 100 units but gets 119 units (19% extra). When selling, he charges the customer for 100 units at cost price but actually gives only 85 units (15% less than 100). The difference between what he pays per actual unit and what he collects per actual unit gives the effective profit percentage. Profit factor is computed as selling price per actual unit divided by cost price per actual unit, and profit percentage is then derived from that ratio.

Step-by-Step Solution:
Step 1: Assume nominal cost price per unit = Re. 1 for simplicity.Step 2: Wholesaler billing: retailer pays for 100 nominal units at Re. 1 each, so money paid = Rs. 100.Step 3: Actual quantity received from wholesaler = 100 + 19% of 100 = 119 units.Step 4: Effective cost price per actual unit = Total cost / Actual quantity = 100 / 119.Step 5: When selling, retailer charges customers for 100 nominal units at Re. 1 each, so revenue per nominal 100 units = Rs. 100.Step 6: But he actually delivers only 100 - 15% of 100 = 85 units.Step 7: Effective selling price per actual unit = 100 / 85.Step 8: Profit factor per actual unit = (Effective selling price per unit) / (Effective cost price per unit).Step 9: Profit factor = (100 / 85) divided by (100 / 119) = (100 / 85) * (119 / 100) = 119 / 85.Step 10: Convert 119 / 85 to decimal: 119 / 85 = 1.4.Step 11: Hence profit percentage = (1.4 - 1) * 100 = 0.4 * 100 = 40%.

Verification / Alternative check:
To verify, we can compute actual amounts for a larger example. Suppose the retailer repeats this process many times, so total effective cost is some multiple of 100 / 119 and total revenue is some multiple of 100 / 85 per unit. Since the ratio of selling price to cost price per unit remains 119 / 85, the profit percentage will always be 40%. Therefore, it does not matter what initial quantity we assume; the result is consistent and robust.

Why Other Options Are Wrong:

• 35%: This underestimates the combined effect of getting extra goods and giving short quantity to customers.
• 42%: Slightly more than the correct value but does not match the precise ratio 119 / 85.
• 46%: This is far from the true computed profit and has no algebraic justification from the given data.

Common Pitfalls:

• Calculating profit on the nominal 100 units instead of actual units received and delivered.
• Forgetting that the retailer gains in two ways simultaneously and incorrectly adding or subtracting percentages linearly.
• Using average of 19% and 15% as the profit percentage, which is conceptually incorrect.

Final Answer:
The retailer earns an effective profit of 40% by cheating in both purchase and sale quantities while keeping the displayed price at cost price.