Profit and Loss is essentially applied percentage — the same multiplication machinery, just wearing a different costume. Once you see it that way, half the battle is won.
Here is the core idea. Every transaction has a Cost Price (CP) — what the seller pays to acquire the goods — and a Selling Price (SP) — what the buyer pays. The difference between them determines profit or loss.
Notice something important: profit and loss percentage is always calculated on CP, not SP. This trips up a large number of test-takers who instinctively use SP as the base. Burn this in.
Now, a real market has a third price: the Marked Price (MP), also called the List Price or MRP. The shopkeeper marks his goods above CP to create headroom. He then offers a discount on MP to the customer. What the customer actually pays is the SP.
Think of it like this: a textile shop has a tag showing ₹1000 on a shirt. That is MP. You negotiate or a sale gives you 20% off. You pay ₹800. That ₹800 is SP. What the shopkeeper paid to the manufacturer — say ₹600 — is CP. His profit = ₹800 − ₹600 = ₹200.
The chain of relationships:
CP → (markup) → MP → (discount) → SP
And the formulas connecting them:
MP = CP × (1 + markup%/100)SP = MP × (1 − discount%/100)SP = CP × (1 + profit%/100) [when profit]SP = CP × (1 − loss%/100) [when loss]For SSC CGL, you will see a steady 3−4 questions from this topic in Tier-1 Quant. The question types are predictable: same SP different outcomes, ratio-based questions, faulty weights, and MP/discount/profit combinations. The concepts do not change — your speed on converting between these forms does.
Stop computing profit as a separate step and adding it. Use multipliers.
In reverse:
This single habit will save you 10−15 seconds per question.
This is SSC's favourite trick. "Two articles are sold at the same SP — profit on one, loss on the other at the same percentage."
Look — when the percentage is the same in both cases, there is always a net loss, and it equals:
If both gain/loss% = 10%: Net loss% = 100/100 = 1%. If both = 20%: Net loss% = 400/100 = 4%.
This formula is derived from the fact that the CP of the loss-making item is always higher than the CP of the profit-making item at the same SP. The total CP always exceeds total SP.
When CP:SP = a:b, profit% = ((b−a)/a) × 100. No variables needed.
CP:SP = 4:5 → Profit% = (1/4) × 100 = 25%. CP:SP = 5:6 → Profit% = (1/5) × 100 = 20%. CP:SP = 3:4 → Profit% = (1/3) × 100 = 33.33%.
Similarly, if SP of n articles = CP of m articles:
SP of 15 = CP of 20 → Profit% = (20−15)/15 × 100 = 5/15 × 100 = 33.33%.
A seller claims to sell at cost price but gives less weight. The profit is on the actual goods delivered.
If he gives x grams instead of 1000g:
He gives 900g instead of 1000g → Profit% = 100/900 × 100 = 11.11%.
Intuition: He buys 900g worth of goods but charges for 1000g worth. His "investment" is 900g units, his "return" is 1000g units. Net gain = 100 on base 900.
Two discounts of a% and b% are NOT simply (a+b)%. The effective single discount is:
Discounts of 20% and 10%: Effective = 20 + 10 − (200/100) = 28%, not 30%.
The most common "hard-looking" question type is actually just two multipliers applied in sequence:
Or working backwards from a target profit%:
So if a dealer wants 20% profit and gives 20% discount: MP/CP = 1.20/0.80 = 1.5 → He must mark 50% above CP.
Marked price = 1.5 × CP. If CP = 800 → MP = 1200. Discount of 20% → SP = 960. Profit = 160 on 800 = 20%. Verified.
When two items are sold at the same SP with equal profit% on one and loss% on the other, the net result is always a loss. Formula: Loss% = (common%)²/100. For SSC CGL questions using 10%: Loss% = 100/100 = 1%. Standard method: compute both CPs, add, compare to total SP (4 steps, ~45s). Shortcut: write down (10)²/100 = 1% loss in 8 seconds. The step count drops from 6 arithmetic operations to 1.
When SP of N articles = CP of M articles, profit% = (M−N)/N × 100 if M > N (profit) or (N−M)/N × 100 if N > M (loss). SP of 15 = CP of 20: profit% = 5/15 × 100 = 33.33% — done in one line. Standard method: assume CP per article = ₹1, compute SP per article, find profit per article, compute percentage (4 steps, ~40s). Shortcut: plug into formula, one fraction, ~10s.
When a seller uses weight x instead of 1000g but charges full price: Profit% = (1000 − x)/x × 100. For 900g weight: (100/900) × 100 = 100/9 = 11.11%. Standard method: set up CP = 900 units, SP = 1000 units, compute profit on base (3 steps, ~30s). This single formula replaces all setup steps and delivers the answer in ~8 seconds — a saving of 3 arithmetic operations.
CP:SP = a:b → Profit% = (b−a)/a × 100. Write the ratio, subtract, divide, multiply — that is it. CP:SP = 4:5 → (5−4)/4 × 100 = 25%. No need to assign variables or solve equations. Standard method: let CP = 4x, SP = 5x, profit = x, profit% = x/4x × 100 (4 steps, ~30s). Shortcut: directly from ratio, 2 arithmetic steps, ~8s.
For any MP-discount-profit question: SP = MP × (1 − d%) and CP = SP / (1 + p%). Chain them: CP = MP × (1 − d%) / (1 + p%). Given MP = 600, discount = 20%, profit = 20%: CP = 600 × 0.8 / 1.2 = 480 / 1.2 = ₹400. Two division steps, no intermediate variable needed. Standard method: compute SP first, write it down, then compute CP from SP (2 separate calculations with risk of error). Multiplier chain does it in one continuous computation, saving one write-down step and ~15 seconds.
Read the question and immediately classify it into one of five types:
Type 1 — Direct CP/SP given, find profit% or loss%: Use (SP−CP)/CP × 100. Done.
Type 2 — Ratio of CP to SP given: Apply (b−a)/a × 100. One step.
Type 3 — Same SP, equal gain/loss%: Apply (common%)²/100 = loss%. Do not compute individual CPs.
Type 4 — SP of N articles = CP of M articles: Apply (M−N)/N × 100. Identify M and N from the sentence, plug in.
Type 5 — MP, discount, profit combination: Build the two-multiplier chain. SP = MP × (1−d%), CP = SP/(1+p%). Reverse if asked for something else.
Type 6 — Faulty weight: Use (1000−x)/x × 100.
If a question looks unfamiliar, reduce it to ratios. Almost every profit-loss question can be solved by setting CP = 100 and tracking what SP becomes. When you do not know where to start, start there.
Why this question: The classic same-SP trap. SSC repeats this structure almost every year with different percentages.
Solving path: Identify this as a same-SP, same-% question immediately. Apply Loss% = (10)²/100 = 1% loss. If you want to verify: CP₁ = 1980/1.1 = ₹1800, CP₂ = 1980/0.9 = ₹2200. Total CP = ₹4000, Total SP = ₹3960. Loss = ₹40. Loss% = 40/4000 × 100 = 1%. Both routes confirm option (A).
Why this question: Tests whether you know the SP-of-N equals CP-of-M shortcut. Without it, students waste time setting up equations.
Solving path: SP of 15 = CP of 20. M = 20, N = 15. Profit% = (20−15)/15 × 100 = 500/15 = 33.33%. Select option (B). Entire solution: one fraction.
Why this question: Standard MP-discount-profit combination. Tests the two-multiplier chain.
Solving path: SP = 600 × 0.8 = ₹480. CP = 480/1.2 = ₹400. Select option (A). Two multiplier steps, no equation setup required.
Why this question: Faulty weight is a recurring SSC question type. The answer is never intuitive — 11.11% feels wrong to most students who guess 10%.
Solving path: He gives 900g, charges for 1000g. Profit% = (1000−900)/900 × 100 = 100/900 × 100 = 11.11%. The trap is that students compute 100/1000 × 100 = 10%, using the wrong base. The base is always what he actually paid for — 900g.
Why this question: Tests CP:SP ratio to profit% conversion. Appears in SSC CGL with minor variations almost every cycle.
Solving path: CP:SP = 4:5. Profit% = (5−4)/4 × 100 = 25%. Select option (B).
Using SP as the base for profit%: Profit and loss percentages are always on CP. SP in the denominator is a different calculation (used in backward problems only when CP is unknown). If you see "profit% on SP", the question will say so explicitly — and SSC rarely asks that.
Adding successive discounts directly: A 20% discount followed by 10% discount is not 30% off. It is 28% off. Use the formula a + b − ab/100 or apply multipliers sequentially: 0.80 × 0.90 = 0.72, meaning 28% effective discount.
Same SP trap: assuming no gain no loss: When the same profit% and loss% are applied at the same SP, the naive answer "they cancel out" is wrong. There is always a net loss. The shopkeeper with the loss sells at a higher CP, so the loss dominates.
Faulty weight: using 1000 as the base: In a 900g-for-1000g fraud, the profit% denominator is 900 (what he invested), not 1000 (what he charged for). Students who divide by 1000 get 10% — a trap option SSC always includes.
Confusing markup% and profit%: "Marked 25% above CP" means MP = 1.25 × CP. Profit% after discount is not 25% — it depends on the discount rate. Mark percentage and profit percentage are only equal when there is no discount.
Applying the loss formula when goods are traded (SP of N = CP of M): When N > M, it is a loss situation. The formula becomes (N−M)/N × 100 loss. Students sometimes mechanically compute (M−N)/N and get a negative number without realising what it means.