Profit and Loss is fundamentally about the relationship between three numbers: what you paid (Cost Price), what you charged (Selling Price), and what was originally advertised (Marked Price). The exam never asks you to memorise formulas — it asks you to see relationships fast.
Here is the core mental model that makes everything click: think of CP as the anchor at 100%. Every other value — SP, MP, discount, profit — is a percentage deviation from that anchor.
So when a question says "marked 30% above CP and sold at 10% discount", you don't need separate formulas. You convert directly:
That single multiplication gives you a 17% profit without invoking any named formula.
The analogy that works in the exam hall: imagine CP as the ground floor of a building. Markup takes you up some floors (MP). Discount brings you down some floors. Where you land is SP. If SP > CP, you're above ground = profit. If SP < CP, you're below ground = loss.
The key insight — discount is always on MP, profit/loss is always relative to CP. This distinction trips up more aspirants than any calculation error. Never take discount on CP, never measure profit on MP.
One more relationship worth internalising before you go deeper: if profit% = loss% in two transactions, the net result is always a loss. Specifically, if you sell two items each at ₹x, one at p% profit and one at p% loss, the combined loss% = p²/100. SBI PO has set questions on this pattern across multiple years.
Stop writing Profit% = (SP - CP)/CP × 100 every time. Build the multiplier habit instead:
This means for a standard markup-discount problem:
SP = CP × (1 + m/100) × (1 - d/100)
where m = markup%, d = discount%. The profit% on CP is then just [(1 + m/100)(1 - d/100) - 1] × 100.
When two discounts d₁ and d₂ are applied one after the other, the equivalent single discount is:
Effective discount = d₁ + d₂ - (d₁ × d₂)/100
Example: 20% then 35% → 20 + 35 - (20 × 35)/100 = 55 - 7 = 48%. So the buyer pays 52% of MP.
This is directly tested in PYQs (see the 2016 question below). Don't do two separate multiplications in the exam — compute the effective multiplier once: 0.80 × 0.65 = 0.52, then divide the given SP by 0.52 to get MP.
A question type that appeared in SBI PO 2025: two articles with different CPs, and the profit amount (not percent) is equal. This is an algebraic setup that resolves cleanly if you assign CP of one article a round number.
Standard move: let CP of the cheaper article = 100 (as a variable unit). Express everything else in terms of that. The "equal profit amount" condition then gives you the ratio of SPs, from which you can find the actual SP and hence profit%.
When two items are bought at equal price but sold at different profit percentages, and you know the combined profit%, you can use the allegation / weighted average approach to find the missing individual profit%. This is cleaner than setting up two equations. The 2019 PYQ (bags question) is a direct application — average of 10% and x% = 13%, so x = 16% by simple symmetric allegation.
If SP₁ gives a profit equal in rupees to the loss in SP₂:
SP₁ - CP = CP - SP₂
CP = (SP₁ + SP₂) / 2
This is the single fastest solve in profit-loss. The 2015 PYQ (article at ₹878 and ₹636) resolves in one line.
Many SBI PO questions give SP and ask for CP. The standard error is to apply the percentage on SP instead of CP. Look — if profit is 20%, then SP = 1.2 × CP, so CP = SP / 1.2, not SP × 0.8. The latter gives you 80% of SP, which is not the CP.
Build this as a reflex: always divide SP by the multiplier to get CP.
CP = SP / (1 ± profit% or loss% as decimal)
For any markup + discount problem, multiply the two multipliers directly on CP.
Markup 30%, discount 10%: SP = CP × 1.30 × 0.90 = CP × 1.17 → 17% profit.
Write the chain left to right in 5 seconds. Compare to standard method: write MP formula, substitute, write SP formula, substitute, compute profit — that's 4-5 steps (~40s). Multiplier chain: 2 steps (~10s).
When profit rupees = loss rupees at two different SPs, CP = arithmetic mean of those two SPs.
CP = (SP₁ + SP₂) / 2. No algebra needed.
Example: profit at ₹878, loss at ₹636 → CP = (878 + 636)/2 = 1514/2 = ₹757. Standard algebraic route: 3 steps (~30s). This: 1 step (~8s).
Two discounts d₁ and d₂ → net multiplier = (1 - d₁/100)(1 - d₂/100).
For 20% and 35%: 0.80 × 0.65 = 0.52. Buyer pays 52% of MP. To recover MP from SP: MP = SP / 0.52.
Avoids computing effective discount% separately and then applying it again — saves 2 arithmetic operations (~15s versus ~35s for two-stage approach).
Two items at same CP sold at different profit percentages p₁ and p₂, overall average profit = p_avg.
Draw allegation cross: (p_avg - p₁) and (p₂ - p_avg) give the ratio of quantities. When quantities are equal (one item each), the relationship simplifies to p_avg = (p₁ + p₂)/2.
So missing profit% = 2 × p_avg - p₁.
In the bags PYQ: 2 × 13 - 10 = 16%. Arrived in 3 seconds versus setting up and solving two equations (~50s).
When a question gives you the rupee difference between two profit scenarios and you have the profit percentages, divide rupee difference by the percentage-point difference to get 1% of CP, then scale.
In the bags PYQ: overall profit 13%, bag 1 at 10%, bag 2 at 16%. The difference between bag 2 and overall = 3%. Given that 3% of CP = ₹90, CP = ₹90/0.03 = ₹3000.
This is the unit method — find what 1% equals, then multiply. Works for any rupee-difference given in profit/loss questions. Saves you from writing full equations.
In the exam hall, run this decision tree in under 10 seconds before writing anything:
Step 1 — Identify what's given and what's asked. Are you given CP and asked SP? Use multiplier. Given SP and asked CP? Divide by multiplier. Given MP and discount? Multiply by (1 - d/100) for SP.
Step 2 — Is profit/loss in rupees or percent? Rupees given → set up unit variable (let 1% of CP = ₹k). Percent given → use multiplier directly.
Step 3 — Is it a two-article or two-transaction problem? Same CP + different profit% → allegation. Same profit/loss amount at different SPs → symmetric average.
Step 4 — Successive discounts? Multiply the multipliers. Never add the percentages directly.
Step 5 — Sanity check. Markup > discount → profit. Markup < discount → loss. If your answer says 170% profit or 100% profit, don't second-guess — these are deliberately high values in SBI PO to test if you doubt yourself.
Why this question: Tests the equal-profit-amount condition with a ratio twist — a 2025-level difficulty pattern that requires you to handle CP ratio and SP ratio simultaneously.
Solving path: Let CP of Q = 100 units, so CP of P = 130 units (30% more). Let SP of P = 10k. Then SP of Q = 9k (90% of SP of P). Equal profit condition: 10k - 130 = 9k - 100. Solving: k = 30. So SP of Q = 9 × 30 = 270, CP of Q = 100. Profit% on Q = (270 - 100)/100 × 100 = 170%.
Why this question: Classic markup-discount with a rupee-difference condition. Tests the unit-variable method under the markup framework.
Solving path: Let CP = 100x, MP = 150x. SP at 15% discount = 150x × 0.85 = 127.5x. SP at 25% discount = 150x × 0.75 = 112.5x. Profit difference = 127.5x - 112.5x = 15x = ₹90. So x = 6. CP = 100 × 6 = ₹600.
Why this question: Multi-condition problem — original SP from markup/discount, then a hypothetical scenario that defines a new profit%. Two unknowns resolve from one equation.
Solving path: Actual SP = 1.30 × 0.90 × x = 1.17x. Under new conditions: new CP = x - 50, new SP = 1.17x + 66, profit = 100% means new SP = 2 × new CP. So 1.17x + 66 = 2(x - 50) = 2x - 100. Therefore 166 = 0.83x, giving x = 200. Actual SP = 1.17 × 200 = ₹234.
Why this question: Equal-cost, unequal-profit problem solved fastest via allegation. Tests whether you reach for equations or the smarter average-based approach.
Solving path: Same CP for both bags. Bag 1: 10% profit. Overall: 13% profit. Since equal quantities, profit% on Bag 2 = 2 × 13 - 10 = 16%. Now, Bag 2's SP - Bag 1's SP = ₹90. SP of Bag 1 = 1.10 × CP. SP of Bag 2 = 1.16 × CP. Difference = 0.06 × CP = ₹90. CP = ₹3000 (per bag).
Why this question: Direct successive-discount reversal. Given final payment, find MP. Pure multiplier application.
Solving path: Net multiplier = 0.80 × 0.65 = 0.52. Buyer pays 52% of MP. MP = 1300 / 0.52 = ₹2500.
Why this question: The symmetric SP pattern in its purest form. One of the fastest solves in profit-loss.
Solving path: Profit at ₹878 = Loss at ₹636 means CP is equidistant from both. CP = (878 + 636)/2 = 1514/2 = ₹757.
Applying discount on CP instead of MP. Discount is always on Marked Price. If a question says "15% discount", that 15% comes off MP, not CP. This single confusion can make you pick the wrong option even when your arithmetic is right.
Dividing instead of multiplying (and vice versa) when recovering CP from SP. If SP = 1.2 × CP, then CP = SP ÷ 1.2, not SP × 0.8. The latter gives 80% of SP, which is a completely different number.
Adding successive discount percentages. 20% + 35% is not 55% combined discount. The actual effective discount is 48%. Always multiply the multipliers: 0.80 × 0.65 = 0.52.
Confusing profit amount with profit percent. Equal profit amount does not mean equal profit percent. In the 2025 PYQ, both articles give the same rupee profit but vastly different profit percentages because their CPs differ. Read the question word for word.
Doubting large profit percentages. SBI PO routinely places answers like 150%, 170%, 100% for profit%. These are not typos or traps — they test whether you trust your calculation. Do the work, verify the algebra, and commit.
Using overall SP to compute profit% instead of individual CP. In two-article problems, always track each article's CP separately. Do not sum both SPs and divide by total CP unless the question asks for overall profit%, in which case that is the exact method — but not for individual profit%.