Math Problem Statement

A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain percent is:

Solution

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Math Problem Analysis

Mathematical Concepts

Percentage Profit and Loss
Discount Calculation
Selling Price and Cost Price Relationship

Formulas

Marked Price (MP) = Cost Price (C) + 20% of C = 1.2C
Selling Price for portion sold at marked price = 0.6C
Selling Price for portion sold at 20% discount = 0.24C
Selling Price for portion sold at 40% discount = 0.18C
Total Selling Price = 1.02C
Gain Percent = (Total Gain / Cost Price) * 100 = 2%

Theorems

Profit and Loss Theorem

Suitable Grade Level

Grades 9-12