Profit & Loss — RRB NTPC Mathematics
This topic carries roughly 10% of Mathematics's 30 questions — tied for the section's heaviest topic alongside Percentage, which it builds on directly. Every profit/loss calculation is a percentage-change calculation with cost price and selling price in place of "old value" and "new value."
1. What RRB NTPC actually asks
Expect direct profit%/loss% calculations from CP and SP, finding CP or SP given the other and the profit/loss percentage, marked-price-and-discount problems, successive discount problems, and word problems involving a mismatch between the number of articles bought and sold at cost versus selling price.
2. The core formulas
Profit = SP − CP (when SP > CP). Loss = CP − SP (when CP > SP).
Profit% = (Profit/CP) × 100. Loss% = (Loss/CP) × 100. Profit and loss percentages are always calculated on the cost price, never on the selling price.
SP = CP × (1 + profit%/100), or CP × (1 − loss%/100) for a loss.
3. Marked price and discount
Marked price (MP) is the listed/labelled price before any discount. Selling price (SP) = MP × (1 − discount%/100).
A markup followed by a discount does not simply cancel. If CP is marked up by m% to get MP, and then MP is discounted by d% to get SP, the net effect on CP is SP = CP × (1 + m/100) × (1 − d/100) — apply the successive-percentage-change logic from the Percentage chapter, not simple subtraction of m and d.
Worked examples
Q1. A shopkeeper buys an article for ₹800 and sells it for ₹920. What is the profit percentage?
Pick an option to check your answer.
Show explanation
Solution. Profit = SP − CP = 920 − 800 = 120. Profit% = (120/800) × 100 = 15%.
A common error is calculating the percentage on the selling price (120/920) instead of the cost price — profit and loss percentages are always on CP. Answer: (b).
Q2. A shopkeeper marks his goods 40% above cost price and then offers a 10% discount on the marked price. What is his actual profit percentage?
Pick an option to check your answer.
Show explanation
Solution. Let CP = 100. Marked price = 100 × 1.4 = 140. SP after 10% discount = 140 × 0.9 = 126.
Profit = 126 − 100 = 26, so profit% = 26%. A common error is subtracting the discount from the markup directly (40% − 10% = 30%), ignoring that the discount applies to the marked price, not the original cost. Answer: (c).
5. Common traps
- Calculating profit/loss percentage on the selling price instead of the cost price. The formula's denominator is always CP.
- Subtracting a markup and discount percentage directly (e.g., 40% markup − 10% discount = 30% profit). This ignores that the discount applies to the marked price, a different base than the original cost — use the successive-multiplication method instead.
- Confusing marked price with selling price. MP is before any discount; SP is after — they're equal only when no discount is offered.
- Getting the article-count mismatch direction backward. If CP of 20 articles equals SP of 25 articles, the seller is receiving LESS per article than they paid (since more articles were needed to match the same total value), meaning a loss, not a profit.
6. Guessing strategy
A quick directional check — does a markup-then-discount problem's net result make sense as a small profit, breakeven, or small loss, given the two percentages involved — often eliminates options with an implausibly large profit or loss.
Summary
- Profit & Loss is roughly 10% of Mathematics's 30 CBT 1 questions — tied for the heaviest topic alongside Percentage.
- Profit% and Loss% are always calculated on cost price (CP), never on selling price.
- SP = CP × (1 + profit%/100) for a profit, or CP × (1 − loss%/100) for a loss.
- A markup followed by a discount requires successive multiplication (like successive percentage change), never simple subtraction of the two percentages.
- Marked price (before discount) and selling price (after discount) are different quantities unless the discount is zero.
- Article-count-mismatch problems (CP of X articles = SP of Y articles) need careful attention to which direction represents profit versus loss.
