1. The problem involves understanding basic calculations related to ratios, percentages, profit, loss, discount, and related concepts. 2. Key formulas and concepts: - Ratio equivalent: If $a:b = c:d$, then $ad = bc$. - Multiplying factor for percentage change: For an increase of $p\%$, multiply by $1 + \frac{p}{100}$; for a decrease of $p\%$, multiply by $1 - \frac{p}{100}$. - Successive percentage changes: Multiply the factors for each change. - Profit = Selling Price (SP) - Cost Price (CP). - Loss = Cost Price (CP) - Selling Price (SP). - Markup = Selling Price - Cost Price. - Discount = Marked Price - Selling Price. 3. Example: If an item costs 100 and is sold at a 20% profit, the selling price is calculated as: $$ SP = CP \times \left(1 + \frac{20}{100}\right) = 100 \times 1.2 = 120 $$ 4. If a discount of 10% is given on the marked price of 150, the selling price is: $$ SP = 150 \times \left(1 - \frac{10}{100}\right) = 150 \times 0.9 = 135 $$ 5. For successive changes, e.g., a 10% increase followed by a 20% decrease: $$ \text{Net factor} = 1.1 \times 0.8 = 0.88 $$ This means an overall 12% decrease. 6. Faulty weights affect the effective price and profit calculations by altering the actual quantity. These concepts form the basis for solving word problems involving profit, loss, discount, and percentage changes.