Profit and Loss — RRB NTPC Study Notes

Overview

Profit and Loss is a high-weightage topic in RRB NTPC Mathematics, with 2–4 questions consistently appearing in every exam. The topic revolves around commercial transactions: buying goods at a **Cost Price (CP)**, selling them at a **Selling Price (SP)**, and calculating the profit or loss. You'll also encounter **Marked Price (MP)** and **discount** scenarios where shopkeepers mark prices higher than CP and then offer discounts to attract buyers.

Mastering this topic requires fluency with percentage calculations and the ability to set up equations quickly. Most errors occur when students confuse CP with MP, misapply successive discount formulas, or make sign errors in profit-loss calculations. The good news: once you memorize 5–6 core formulas and practice 15–20 problems, you can solve any RRB-level question in under 90 seconds. This topic connects naturally to Percentage and Ratio-Proportion, so revise those chapters first if you're rusty.

Focus on understanding the logical flow: CP → add profit or subtract loss → get SP. Or: MP → apply discount → get SP. Real exam questions test your speed in converting word problems into these equations and calculating percentages mentally.

Key Concepts

• **Cost Price (CP)**: The amount paid to acquire or produce a good. This is your baseline for profit or loss calculations.
• **Selling Price (SP)**: The amount received when the good is sold. If SP > CP, there's a profit; if SP < CP, there's a loss.
• **Profit**: Profit = SP − CP. Always expressed as a positive number. Profit% = (Profit / CP) × 100.
• **Loss**: Loss = CP − SP. Loss% = (Loss / CP) × 100. Note the percentage is always calculated on CP, not SP, unless stated otherwise.
• **Marked Price (MP)**: The price tag on an item before any discount. Shopkeepers mark goods above CP to absorb discount and still earn profit.
• **Discount**: Reduction offered on the Marked Price. Discount = MP − SP. Discount% = (Discount / MP) × 100. The discount percentage is always on MP.
• **Successive Discounts**: Two or more discounts applied one after another. You cannot simply add the percentages; use the formula: Net% = d₁ + d₂ − (d₁ × d₂)/100 for two discounts d₁% and d₂%.
• **Break-even**: When SP = CP, there is neither profit nor loss. Break-even problems often involve finding the number of items to sell or the price to charge.

Formulas / Key Facts

1. **SP when profit% is known**: SP = CP × (100 + Profit%) / 100 *Add the profit percentage to 100, then take that fraction of CP.*

2. **SP when loss% is known**: SP = CP × (100 − Loss%) / 100 *Subtract the loss percentage from 100, then take that fraction of CP.*

3. **CP when SP and profit% are known**: CP = SP × 100 / (100 + Profit%) *Rearranging formula 1 to solve for CP.*

4. **CP when SP and loss% are known**: CP = SP × 100 / (100 − Loss%) *Rearranging formula 2 to solve for CP.*

5. **Profit% or Loss%**: Profit% = [(SP − CP) / CP] × 100. If result is negative, it's a loss percentage.

6. **SP from MP and Discount%**: SP = MP × (100 − Discount%) / 100 *Apply discount on the marked price to get selling price.*

7. **Successive Discount Net%**: For two discounts d₁% and d₂%, Net Discount% = d₁ + d₂ − (d₁ × d₂)/100 *Then apply this net% to the MP using formula 6.*

8. **Relation among CP, MP, Discount, Profit**: MP = CP × (100 + Profit%) / (100 − Discount%) *Useful when a shopkeeper marks x% above CP and offers y% discount to earn z% profit.*

Worked Examples

**Example 1**: A shopkeeper buys an article for ₹500 and sells it for ₹650. Find the profit percentage. *Solution*: Profit = SP − CP = 650 − 500 = ₹150. Profit% = (Profit / CP) × 100 = (150 / 500) × 100 = 30%. **Answer: 30% profit.**

**Example 2**: An article is marked 40% above its cost price. A discount of 20% is offered on the marked price. Find the overall profit or loss percentage. *Solution*: Let CP = ₹100. MP = 100 + 40% of 100 = 100 + 40 = ₹140. Discount = 20% of MP = 20% of 140 = 28. SP = MP − Discount = 140 − 28 = ₹112. Profit = SP − CP = 112 − 100 = ₹12. Profit% = (12 / 100) × 100 = 12%. **Answer: 12% profit.**

**Example 3**: A trader allows successive discounts of 10% and 20% on an article marked at ₹5000. What is the final selling price? *Solution*: Net Discount% = 10 + 20 − (10 × 20)/100 = 30 − 2 = 28%. SP = MP × (100 − 28) / 100 = 5000 × 72 / 100 = ₹3600. Alternatively, apply step-by-step: After 10% discount: 5000 × 90/100 = ₹4500. After 20% discount on ₹4500: 4500 × 80/100 = ₹3600. **Answer: ₹3600.**

Common Mistakes

• **Calculating percentage on SP instead of CP for profit/loss**: Always remember profit% and loss% are based on Cost Price unless explicitly stated otherwise. Students often compute (SP − CP)/SP, which is incorrect.

• **Adding successive discounts directly**: If discounts are 10% and 20%, the net discount is not 30%. Use the formula d₁ + d₂ − (d₁ × d₂)/100. Direct addition underestimates the selling price.

• **Confusing MP with CP**: When a question states "marked 30% above cost price," students sometimes apply discount on CP instead of MP. Always: CP → calculate MP → apply discount → get SP.

• **Sign errors in loss scenarios**: When loss occurs, SP < CP. Students sometimes write Profit = CP − SP and get confused with signs. Stick to: Loss = CP − SP (positive value), then Loss% = (Loss/CP) × 100.

• **Forgetting to convert percentages**: Writing 20% as 20 instead of 0.20 in multiplications. Use the formula format (100 ± x)/100 to avoid this error.

Quick Reference

• **Profit = SP − CP; Loss = CP − SP**. Base percentages on CP.
• **SP = CP × (100 ± Profit or Loss %) / 100**. Use + for profit, − for loss.
• **Discount is always on Marked Price (MP)**, not on CP or SP.
• **Successive discounts d₁% and d₂%: Net% = d₁ + d₂ − d₁×d₂/100**.
• **To find CP from SP and profit%: CP = SP × 100 / (100 + Profit%)**.
• **Practice mental calculation of 10%, 20%, 25% and 50% to save time in exams.**

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**Pro Tip**: In the exam, if an exact calculation is tedious, use the answer choices to backsolve. Assume one option is correct, compute SP or CP, and verify against the question. This technique works beautifully for profit-loss MCQs in RRB NTPC.