Markup, discount, and short-weighing — A trader marks goods up by 80% over cost and then offers a 25% discount on the marked price. In addition, he delivers 10% less quantity than charged (short-weighing). What is his net profit percentage on cost?

Introduction / Context: Combining markup and discount changes the selling price per nominal unit, while short-weighing changes the delivered quantity for that price. Converting all effects into a price per true unit versus cost per true unit gives the net profit percentage cleanly.

Given Data / Assumptions:

• MP = 1.80 * CP (80% markup).
• Offered discount = 25% ⇒ SP per nominal unit = 0.75 * MP.
• Delivered quantity per nominal unit = 0.90 (10% short-weigh).

Concept / Approach: Compute SP per true unit by dividing price per nominal unit by the delivered fraction. Then compare to CP per true unit (which is simply CP) to obtain profit% = (SP_true − CP)/CP * 100.

Step-by-Step Solution:

Verification / Alternative check: For CP = ₹ 100 per true kg, nominal customer bill per “kg” is ₹ 135 but receives only 0.9 kg ⇒ ₹ 150 per true kg, matching 50% profit.

Why Other Options Are Wrong: 35%, 40%, 45%, and 55% do not reflect the compounded effect of markup, discount, and short-weighing.

Common Pitfalls: Applying 25% discount to cost instead of to the marked price, or ignoring the short-weigh factor when converting to true per-unit revenue.

Final Answer: 50%