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.*