Profit and Loss is the language of trade. Every transaction has two prices that matter: what you paid (Cost Price, CP) and what you received (Selling Price, SP). The difference between them determines whether you walked away richer or poorer.
Here is the simple picture: imagine you buy a second-hand phone for ₹4,000 and sell it to a friend for ₹5,000. You made a profit of ₹1,000. Now flip it — you bought it for ₹4,000 and sold it under urgency for ₹3,000. You lost ₹1,000. Profit and Loss quantifies this difference as a percentage of what you originally paid (CP), not what you sold it for.
Why CP as the base? Because you are measuring how efficiently your own investment performed. Your ₹4,000 either grew or shrunk — and the percentage tells you by how much.
The third actor in most SSC MTS questions is the Marked Price (MP), also called the Listed Price. This is what the shopkeeper writes on the price tag before giving you a discount. The chain runs:
CP → (add margin) → MP → (subtract discount) → SP
Discount is always calculated on MP. Profit or loss is always calculated on CP. Mixing these two bases is the number-one mistake candidates make.
One more term — Overhead Expenses. Sometimes a problem says the shopkeeper paid ₹100 for a shirt plus ₹20 for transportation. The actual CP becomes ₹120. Always add overhead costs to the purchase price before computing any percentage.
That is the entire conceptual territory. Everything else in this topic is just algebra on top of these three relationships.
You need exactly four relationships. Write them on your palm the first week and you will not need to after that.
Notice both percentages have CP in the denominator. Always.
Stop working with additions and subtractions. Use multipliers. If CP = ₹100 and profit is 25%, then:
If there is a 30% loss:
Reverse: if you know SP and profit%, find CP:
This reverse formula is critical for questions that give you SP and the profit percent, then ask for CP.
When a question involves both a discount on MP and a profit over CP, you have two multipliers working in sequence:
Set them equal when needed:
So:
Look — this single equation solves every "MP and discount with profit" question. Memorise the structure, not the individual steps.
When a question gives you SP:CP as a ratio, compute profit or loss directly from the ratio. If SP:CP = 3:4, then SP = 3 units, CP = 4 units, Loss = 1 unit.
No variables needed. Assign the ratio values directly as amounts.
A special SSC favourite: a shopkeeper sells at CP but cheats on the weight. If the stated weight is W but actual weight given is w (where w < W), the profit comes from giving less goods.
Why? You charge for W grams but give only w grams. Your cost was for w grams, your revenue covers W grams.
For example: stated weight 100g, actual weight 67g.
When SP is increased or decreased by a percentage after an initial loss or profit, work in two steps on an assumed CP of ₹100. Never try to combine percentages with a single formula here — the base shifts and you will get wrong answers.
When SP:CP ratio is given, Loss% = (CP part − SP part) / CP part × 100. For SP:CP = 3:4, loss = 1/4 × 100 = 25%. No algebra, no substitution. Standard method (assign variables, form equation, solve): 40 seconds. This pattern: 8 seconds.
Assume MP = ₹100 whenever the question involves a discount percentage and a profit percentage but no absolute values. Compute SP from discount, then reverse-compute CP from profit. Every intermediate step uses simple arithmetic on 100. Standard method (algebraic simultaneous): 60 seconds. Assumption method: 20 seconds. Saves 3–4 steps.
Any question of the form "sold at X% loss, then price increased by Y%" — set CP = ₹100, find first SP, apply the second multiplier, compare final SP to 100. The difference divided by 100 gives profit or loss percent directly. No formula needed. Step count: 3 steps vs 6 steps algebraically.
Convert recurring percentages to fractions before computing: 33.33% = 1/3, 25% = 1/4, 16.67% = 1/6, 12.5% = 1/8. If CP = ₹300 and loss = 33.33%, loss amount = 300 × 1/3 = ₹100. No long division. For SP:CP = 2:3, loss = 1/3 of CP = 33.33% — spotted instantly. Saves 15–20 seconds per question involving these fractions.
When a dealer gives (100 − x)% of the stated weight while charging full price, profit% = x/(100−x) × 100. For 33% less weight: profit = 33/67 × 100. Memorise the structure — numerator is the shortage, denominator is the actual quantity given. Prevents the classic error of putting shortage in the denominator.
When you see a Profit and Loss question in the exam, run through this decision sequence in 10 seconds before you write a single digit:
Step 1 — What is given?
Step 2 — Are there two sequential changes?
Step 3 — Is a weight-cheat involved?
Step 4 — Check your base.
If the numbers look ugly (like 1680 × 81/100), round and estimate first to eliminate 2–3 options, then compute only to confirm.
Why this question: Ratio questions are a high-frequency pattern in SSC MTS Quant. This one tests whether you know which value is the base.
Solving path: SP:CP = 3:4. Assign SP = 3 units, CP = 4 units. Loss = 1 unit. Loss% = 1/4 × 100 = 25%. Done in under 10 seconds. No algebra required.
Why this question: Sequential percentage changes trip up candidates who try to combine both percentages in one step.
Solving path: Assume CP = ₹100. SP at 30% loss = ₹70. New SP after 50% increase = 70 × 1.5 = ₹105. Since ₹105 > ₹100 (CP), profit = ₹5, so profit% = 5%. The trap: do not average the two percentages — that gives a wrong answer.
Why this question: MP-with-discount-plus-profit questions appear often and require you to hold two multipliers simultaneously.
Solving path: Assume MP = ₹100. After 40% discount, SP = ₹60. This SP gives 25% profit, so CP = 60/1.25 = ₹48. Without discount, SP = MP = ₹100. Profit% = (100 − 48)/48 × 100 = 52/48 × 100 = 108.33%.
Why this question: Straightforward unit-cost question from 2024, but many candidates panic and divide ₹15 by the wrong number.
Solving path: CP per article = ₹15 ÷ 15 = ₹1. SP per article = ₹1.32. Profit = ₹0.32. Profit% = 0.32/1 × 100 = 32%. The distractor here is computing on total values — result is the same, but beginners get confused. Work per unit, it is cleaner.
Why this question: "Fraction of CP lost" questions require you to set up the right equation for CP before calculating the percentage.
Solving path: Let CP = 5x. Loss = two-fifths of CP = 2x. So SP = 5x − 2x = 3x. Given SP = ₹810, so 3x = 810 → x = 270. CP = 5 × 270 = ₹1,350. Loss = ₹540. Loss% = 540/1350 × 100 = 40%.
Why this question: The simplest form of the concept — a clean two-step question that anchors your understanding of the base rule.
Solving path: CP = ₹300, SP = ₹200. Loss = ₹100. Loss% = 100/300 × 100 = 33.33%. Note: the answer is 33.33% loss, not gain. Read the question direction.
Dividing by SP instead of CP. Profit% and Loss% are always calculated as a fraction of CP, not SP. If you divide by SP, you will get a different (wrong) number that is also a valid-looking percentage — making this error hard to self-detect.
Applying discount on CP. Discount is given on Marked Price. A shopkeeper who gives 20% off on an MP of ₹500 reduces the SP to ₹400, not to 80% of CP. Mixing the two bases is the single most common error in MP-discount questions.
Combining sequential percentages by addition or averaging. A 30% loss followed by a 50% increase does not give 20% profit. You must apply each multiplier step by step on the value after the previous change.
Ignoring overhead costs. If a problem says "bought for ₹200 and spent ₹50 on repairs", the CP is ₹250. Computing profit on ₹200 will inflate your profit percentage.
Flipping numerator and denominator in weight-cheat problems. Profit% = shortage / actual-given, not shortage / stated-weight. The denominator is what you actually gave (your real cost base), not the inflated stated figure.
Not checking the answer direction. After computing, confirm whether the result is a profit or a loss before matching to options. Several SSC MTS options include both "X% profit" and "X% loss" as choices with the same numerical value, placed to catch candidates who compute correctly but label incorrectly.