💰 Profit & Loss

Day 1 | ⏱️ Part of 4-Hour Quant Block | TCS Interview Prep

📌 Subtopics

• Cost Price (CP), Selling Price (SP), Marked Price (MP)
• Profit and Loss calculations
• Profit/Loss percentage
• Discount and Successive Discounts
• Dishonest dealer problems
• Buy X Get Y Free problems

📖 Comprehensive Notes

1. Cost Price (CP), Selling Price (SP), & Marked Price (MP)

• Cost Price (CP): The price at which an item is purchased. It is the baseline for calculating profit or loss.
• Selling Price (SP): The price at which an item is sold.
• Marked Price (MP / List Price): The labeled price on an item before any discount.

2. Profit and Loss Calculations

• Profit (Gain): Occurs when $SP > CP$. $\text{Profit} = SP - CP$
• Loss: Occurs when $CP > SP$. $\text{Loss} = CP - SP$

Example: An item bought for $₹800$ is sold for $₹1,000$. $\text{Profit} = 1000 - 800 = ₹200$.

3. Profit/Loss Percentage

Profit and loss percentages are always calculated relative to the Cost Price (CP) unless specified otherwise.

• $\text{Profit \%} = \left(\frac{\text{Profit}}{CP}\right) \times 100$
• $\text{Loss \%} = \left(\frac{\text{Loss}}{CP}\right) \times 100$
• Shortcut Multipliers:
  • For a $20\%$ profit, $SP = 1.2 \times CP$
  • For a $15\%$ loss, $SP = 0.85 \times CP$

Example: Find the loss percentage if an article costing $₹500$ is sold for $₹420$. $\text{Loss} = 500 - 420 = ₹80$. $\text{Loss \%} = \left(\frac{80}{500}\right) \times 100 = 16\%$.

4. Discount and Successive Discounts

• Discount: A reduction offered on the Marked Price (MP). $\text{Discount} = MP - SP$ $\text{Discount \%} = \left(\frac{\text{Discount}}{MP}\right) \times 100$
• Successive Discounts: Multiple discounts applied sequentially. If discounts of $d_1\%$ and $d_2\%$ are given, the equivalent single discount $D\%$ is: $D = d_1 + d_2 - \frac{d_1 \times d_2}{100}$

Example: Find the single equivalent discount for successive discounts of $20\%$ and $10\%$. $D = 20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28\%$.

5. Dishonest Dealer Problems

A dishonest dealer claims to sell goods at CP but uses a false weight that is less than the actual weight.

• $\text{Gain \%} = \left(\frac{\text{Error}}{\text{True Value} - \text{Error}}\right) \times 100$
• Or alternatively: $\text{Gain \%} = \left(\frac{\text{Goods Left/Saved}}{\text{Goods Actually Sold}}\right) \times 100$

Example: A merchant sells his goods at cost price but uses a weight of $900\text{ g}$ instead of $1\text{ kg}$. Find his profit $\%$. $\text{Error} = 1000 - 900 = 100\text{ g}$. $\text{Gain \%} = \left(\frac{100}{900}\right) \times 100 = 11.11\%$.

6. Buy X Get Y Free Problems

For “Buy $X$, Get $Y$ Free” promotions, the customer gets a total of $X + Y$ items, but only pays for $X$ items. The discount is the value of the free items $Y$ over the total marked price of all items. $\text{Effective Discount \%} = \left(\frac{Y}{X+Y}\right) \times 100$

Example: What is the discount percentage of a “Buy 3, Get 2 Free” offer? $\text{Discount \%} = \left(\frac{2}{3+2}\right) \times 100 = \frac{2}{5} \times 100 = 40\%$.

🌐 Learning Resources

✅ Practice Links

📝 Key Formulas

Profit = SP - CP
Loss   = CP - SP
Profit% = (Profit / CP) × 100
Loss%   = (Loss / CP) × 100
SP = CP × (1 + Profit%/100)
SP = CP × (1 - Loss%/100)
Discount% = (Discount / MP) × 100
SP = MP × (1 - Discount%/100)

Tip: If a dishonest dealer claims to sell at CP but uses false weights: Gain% = (Error / True Value - Error) × 100

🔗 Related Topics

• Percentages — Profit/loss calculations are percentage-based
• Ratios and Proportion — Ratio problems in cost/selling price
• Equations — Word problems reducing to equations
• Data Interpretation — Profit/loss analysis in DI sets
• Allegations and Mixtures — Mixture cost problems involve P&L concepts