Profit and Loss: Key Concepts, Formulas, and Solved Examples

Profit and loss questions appear in nearly every campus placement aptitude test, and they reduce to nine patterns once you know the vocabulary cold.

The NCERT Class 8 “Comparing Quantities” chapter provides the foundational definitions. The placement test version extends those into trickier setups: marked prices, discount chains, and traders who use false weights. This article covers all of them with verified arithmetic.

The Three Price Points: CP, SP, and MP

Every profit and loss problem centres on at most three values.

Term	Full form	What it means
CP	Cost Price	What the trader pays to acquire or produce the item
SP	Selling Price	What the trader receives from the buyer
MP	Marked Price	The price written on the label before any discount is applied

Two derived values follow directly:

• Profit = SP minus CP (applies when SP is greater than CP)
• Loss = CP minus SP (applies when CP is greater than SP)

The most common first-draft error is using SP as the base for profit percentage calculations. Both Profit% and Loss% are always calculated on CP in standard aptitude problems, not on SP.

Core Formulas

Six formulas cover the vast majority of questions. The table below states each one and flags the two that are most frequently misapplied.

Formula	Expression	Common trap
Profit%	(Profit / CP) times 100	Using SP as denominator instead of CP
Loss%	(Loss / CP) times 100	Same base error
SP from profit%	CP times (100 + Profit%) / 100	Forgetting to divide by 100
SP from loss%	CP times (100 minus Loss%) / 100	Sign error: subtract, not add
CP from SP and profit%	SP times 100 / (100 + Profit%)	Inverting numerator and denominator
CP from SP and loss%	SP times 100 / (100 minus Loss%)	Sign error in denominator

Percentage problems often accompany profit and loss in the same test section. If you need a refresher on percentage mechanics before working through these examples, FACE Prep’s guide on solving percentage problems with ease covers the base formulas.

Worked Examples: Basic Profit and Loss

Work through each example before reading the solution. The self-check step is where the learning happens.

Example Set 1

• Q1: A trader buys a book for ₹360 and sells it for ₹432. Find the profit percentage.
• Step 1: Profit = 432 - 360 = ₹72
• Step 2: Profit% = (72 / 360) times 100 = 20%
• Answer: 20% profit

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• Q2: A shopkeeper buys goods for ₹1,200 and sells them at a loss of 25%. Find the selling price.
• Step 1: SP = CP times (100 - 25) / 100 = 1200 times 0.75
• Step 2: SP = ₹900
• Answer: ₹900

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• Q3: An article is sold for ₹5,040 at a profit of 12%. Find the cost price.
• Step 1: CP = SP times 100 / (100 + Profit%) = 5040 times 100 / 112
• Step 2: CP = 504000 / 112 = ₹4,500
• Verify: 4500 times 1.12 = 5040
• Answer: ₹4,500

The reverse-calculation formula in Q3, finding CP from SP and profit%, is the single most tested formula pattern in quant aptitude rounds.

Marked Price, Discount, and Successive Discounts

Once a marked price appears in a problem, you are working with three values instead of two: MP, SP, and CP. The relationship is: SP = MP minus Discount. Discount% is always calculated on MP, not CP.

Example Set 2

• Q4: Marked price = ₹1,500. Discount = 20%. Find the selling price.
• Step 1: Discount amount = 1500 times 20 / 100 = ₹300
• Step 2: SP = 1500 - 300 = ₹1,200
• Answer: ₹1,200

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• Q5: A trader marks goods at 50% above cost price and gives a discount of 20%. Find the profit percentage.
• Step 1: Let CP = ₹100
• Step 2: MP = 100 times 1.50 = ₹150
• Step 3: SP = 150 times 0.80 = ₹120
• Step 4: Profit% = (120 - 100) / 100 times 100 = 20%
• Answer: 20% profit

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• Q6: Successive discounts of 30% and 20% on a marked price of ₹2,000. Find the final SP and effective discount percentage.
• Step 1: After first discount: 2000 times 0.70 = ₹1,400
• Step 2: After second discount: 1400 times 0.80 = ₹1,120
• Step 3: Effective discount = (2000 - 1120) / 2000 times 100 = 880 / 2000 times 100 = 44%
• Formula check: 30 + 20 - (30 times 20 / 100) = 50 - 6 = 44%
• Answer: SP = ₹1,120. Effective discount = 44%, not 50%

The formula for any two successive discounts d1 and d2 is: effective discount = d1 + d2 - (d1 times d2 / 100). The subtracted term is always positive, so the effective discount is always less than the arithmetic sum. This is the calculation point where students lose marks by adding the two percentages directly.

Two Patterns Worth Memorising: Same-SP and Dishonest Traders

These two question types appear less often than basic CP/SP problems, but they account for a disproportionate share of the harder questions in rounds like TCS NQT and ZS Associates aptitude test.

The Same-SP Trap

When two items are sold at the same price, one at x% profit and the other at x% loss, the combined result is always a loss. The formula: Loss% = x squared / 100.

• Q7: Two items are each sold for ₹960. The first is sold at 20% profit; the second at 20% loss. Find the overall profit or loss percentage.
• Step 1: For item 1 (profit): CP1 = 960 / 1.20 = ₹800
• Step 2: For item 2 (loss): CP2 = 960 / 0.80 = ₹1,200
• Step 3: Total CP = 800 + 1200 = ₹2,000
• Step 4: Total SP = 960 + 960 = ₹1,920
• Step 5: Loss = 2000 - 1920 = ₹80
• Step 6: Loss% = 80 / 2000 times 100 = 4%
• Formula check: 20 squared / 100 = 400 / 100 = 4%
• Answer: Overall loss of 4%

The Dishonest Trader

A trader who claims to sell at cost price but uses a false weight gains profit from the measurement error alone.

• Q8: A trader uses an 800g weight instead of 1 kg (1,000g) and sells at cost price. Find the profit percentage.
• Step 1: Error = 1000 - 800 = 200g
• Step 2: Profit% = (Error / (True weight - Error)) times 100 = (200 / 800) times 100 = 25%
• Verify: Pays ₹800 for 800g (at ₹1/g), sells it as 1,000g for ₹1,000. Profit = ₹200. Profit% = 200/800 times 100 = 25%
• Answer: 25% profit

P&L in Campus Placement Tests

Profit and loss is a standard topic in campus placement aptitude tests across service-tier and analytics companies. The TCS NQT quant section, for instance, consistently includes at least two to three P&L questions per attempt, which you can confirm on the TCS NQT official page. Companies that weight quant more heavily, such as analytics firms, often include the same-SP and dishonest-trader variants from the last section.

The examples above cover the most frequently tested question types. The remaining variations include buy-N-get-M-free problems (which reduce to a profit percentage on a fractional CP) and cost-price markup chains across multiple traders. Both use the same CP/SP ratio approach demonstrated above.

The same first-principles approach applies to time and work aptitude questions. Re-deriving each formula (rather than memorising it blindly) prevents the careless errors that cost marks under time pressure.

The percentage-chain reasoning that explains why successive discounts never add linearly is the same intuition used when reading AI API pricing models: every new rate applies to the already-adjusted base, not the original. If you want to take these calculation patterns into real AI product work, TinkerLLM offers a ₹299/month sandbox where they become practical debugging tools rather than exam-prep abstractions.