Profit, Loss & Discount

Avoid formulas like $SP = CP(100+P)/100$. Use Ratios.

• 20% Profit: $1/5 \to CP=5, SP=6$.
• 20% Loss: $1/5 \to CP=5, SP=4$.
• Profit on SP: If 20% on SP, $1/5 \to SP=5, Profit=1 \implies CP=4$. Actual P% = $1/4 = 25\%$.

Direct relation between CP, MP, Profit%, and Discount%.

• Formula: $\frac{CP}{MP} = \frac{100 - D\%}{100 + P\%}$.
• Use this when Discount and Profit are given to find MP or CP directly.

Profit comes from using less weight.

• Formula: $\frac{\text{True Weight}}{\text{False Weight}} = \frac{100+P\%}{100\pm x\%}$.
• Logic: If he uses 900g for 1kg, he sells 900g but charges for 1000g. Profit = 100g on 900g CP.

Effective Discount calculation.

• Rule: Free items are the Discount. Total items (Paid + Free) are the MP base.
• $\text{Discount \%} = \frac{\text{Free}}{\text{Total}} \times 100$.

Net price after multiple discounts.

• Formula: $x + y - xy/100$ (Note the signs: $-D_1 - D_2 + D_1D_2/100$).
• Ratio: If 10% and 10% off: $10 \to 9, 10 \to 9 \implies 100 \to 81$. Net 19% off.

Common Scenario: Two items sold at same Price.

• Case A: Same CP. x% Gain, x% Loss $\to$ No Profit No Loss.
• Case B: Same SP. x% Gain, x% Loss $\to$ Always Loss of $x^2/100 \%$.