Profit and Loss is fundamentally a chapter about the gap between what something costs and what it sells for. Every transaction in this chapter has three values that matter: the Cost Price (CP) — what the seller paid to acquire the item, the Selling Price (SP) — what the buyer actually pays, and the Marked Price (MP) — the label price before any discount is applied.
Here is the core logic: if SP > CP, you made a profit. If SP < CP, you took a loss. The percentage is always calculated on the CP (unless a question explicitly tells you otherwise).
Think of it like this — you are a vegetable vendor at Sarojini Nagar market. You bought tomatoes at ₹30/kg (that is your CP). You write ₹50/kg on your sign (that is your MP). A customer bargains, so you agree to ₹40/kg (that is your SP after the discount). Your profit is ₹10 on a CP of ₹30, which is 33.3%.
The marked price and discount layer is where SSC CHSL loves to hide difficulty. Questions will give you the MP and a discount percentage, ask you to find the profit percentage, or flip it entirely — give you the profit percentage and ask what the MP:CP ratio must be. That chain — CP → MP → Discount → SP → Profit% — is the backbone of 60% of the questions in this chapter.
One more concept worth locking in early: dishonest shopkeeper problems. Here the "loss" or "gain" does not come from price manipulation but from weight manipulation. The shopkeeper sells less than the stated quantity. The gain formula for this is specific and frequently tested, so it gets its own trick block below.
Keep the vocabulary straight:
You must be able to rearrange these in your head. If SP and Profit% are given, find CP:
The chain question always has this structure: CP is the base, MP is set above CP by some markup, then a discount brings SP below MP. You need to figure out where SP lands relative to CP.
Suppose CP = 100, markup = 80%, so MP = 180. Discount = 48%, so:
Since SP < CP, there is a loss of 6.4 on CP of 100, giving a loss% of 6.4% = 6\frac{2}{5}\%.
Look — the key insight here is that markup and discount do not cancel neatly. An 80% markup followed by a 48% discount does not give you 32% profit. The discount is calculated on the marked price, not on CP. This is the most common trap in this entire chapter.
For the combined effect of markup (m%) and discount (d%):
If this is positive, it is profit. If negative, it is loss. This formula saves 30-40 seconds on combined markup-discount questions.
When a shopkeeper uses a false weight w grams instead of the true 1000 grams (1 kg), and sells at cost price:
This is derived from the fact that he gives only w grams worth of goods but charges for 1000 grams. The error is (1000 - w) grams. His gain is on an "investment" of only w grams of actual goods.
For a 920 gm weight used instead of 1000 gm:
SSC CHSL loves asking: "After giving x% discount, profit is y%. What is MP:CP?"
The approach: let CP = 100. Then SP = 100 + y. Since SP = MP × (100-x)/100:
Then MP:CP = that value : 100. Simplify. This is a one-step ratio extraction once you have the SP.
If two discounts a% and b% are offered one after another on the same item:
This is the same structure as the markup-discount net formula. Pattern recognition across these two will save you re-deriving from scratch.
A specific question pattern (tested in 2025 CHSL): "Sells X items for ₹P and suffers a loss equal to the SP of Y items." Here:
This structure looks unfamiliar but solves cleanly in under 60 seconds once you recognize it.
When a shopkeeper marks up by m% and gives a discount of d%, the net profit or loss percentage is:
Net% = m − d − (m × d)/100
Positive = profit, negative = loss.
Example: markup 25%, discount 20%. Net% = 25 − 20 − (25×20)/100 = 5 − 5 = 0%. Break-even.
Example: markup 80%, discount 48%. Net% = 80 − 48 − (80×48)/100 = 32 − 38.4 = −6.4%. Loss of 6.4%.
Standard method (set CP=100, compute MP, apply discount, subtract): 5 steps, ~50 seconds. This formula: 3 operations, ~15 seconds.
For a false weight problem: Gain% = (Error ÷ Weight actually given) × 100.
Error = (True weight − False weight). Weight given = False weight.
920 gm used instead of 1 kg: Error = 80, Given = 920. Gain% = 80/920 × 100 = 8.70%.
Students often divide by 1000 (true weight) by instinct — that gives 8%, which is wrong. The denominator is always what the shopkeeper actually gives out, not what he claims.
Standard error (dividing by 1000): wrong answer in same time. This anchor: correct answer, ~10 seconds.
When loss = SP of Y items and total sold = X items at total SP = P:
Step 1: SP per item = P/X. Step 2: Loss = Y × (P/X). Step 3: CP total = P + Loss. Step 4: CP per item = CP total / X.
For "12 pens sold for ₹480, loss = SP of 3 pens": SP/pen = ₹40. Loss = 3×40 = ₹120. CP total = 600. CP/pen = ₹50.
Standard approach (setting up equation with unknown CP, solving): ~70 seconds. This step-by-step substitution: ~25 seconds — no algebra needed.
Given: discount = d%, profit = p%. Find MP:CP.
Set CP = 100. SP = (100+p). MP = SP × 100/(100−d).
Ratio MP:CP = [100×(100+p)/(100−d)] : 100 = (100+p):(100−d).
Example: 10% discount, 20% profit → MP:CP = 120:90 = 4:3.
You do not need to write any equations. Just plug into the ratio directly. Standard method (equation with variables): 3 variable steps, ~45 seconds. This pattern: 2 arithmetic operations, ~12 seconds.
If an item is sold at (n/m) of its usual SP and still makes p% profit:
Let CP = 100. Then (n/m) × usual SP = (100+p). Usual SP = (100+p) × (m/n). Profit at usual SP = usual SP − 100.
Example: sold at 9/10 of usual SP → 20% profit. (9/10) × usual SP = 120 → usual SP = 120 × 10/9 = 133.33. Profit% = 33.33%.
Standard method (two variables): ~60 seconds. This one-line derivation: ~18 seconds.
When you see a Profit and Loss question in the exam hall, run this decision tree in 10 seconds before writing anything:
Step 1 — Identify what is given and what is asked. Is CP given? Is MP given? Is Discount% given? Is Profit% given?
Step 2 — Spot the question type:
Step 3 — Set CP = 100 as default unless the problem gives you an actual CP value. Working with 100 as base eliminates one multiplication step and lets you read off percentages directly.
Step 4 — Avoid quadratic equations. Every question in this chapter at CHSL level solves linearly. If you are setting up x², you have gone off track — restart with CP = 100.
Why this question: This is the classic "loss = SP of some items" pattern that appeared in CHSL 2025. Recognizing the structure immediately tells you the solve path.
Solving path: SP per pen = 480/12 = ₹40. Loss = SP of 3 pens = 3 × 40 = ₹120. Since loss means CP = SP + Loss: CP of 12 pens = 480 + 120 = ₹600. CP per pen = 600/12 = ₹50. The trick is recognizing that "loss equals SP of 3 pens" gives you the loss amount directly — no algebraic equation needed.
Why this question: Tests the MP:CP ratio derivation under a combined discount and profit condition, which is one of the three most tested structures in CHSL Profit and Loss.
Solving path: Set CP = 100. Profit = 20%, so SP = 120. Discount = 10%, so SP = MP × 0.9 = 120, giving MP = 120/0.9 = 400/3. Ratio MP:CP = (400/3):100 = 4:3. Using the shortcut: MP:CP = (100+20):(100−10) = 120:90 = 4:3.
Why this question: This 2024 question uses the "drop in SP = percentage increase in loss" structure to back-calculate the CP — a reverse-engineering approach that trips students who try to forward-solve.
Solving path: The SP dropped from ₹5,000 to ₹4,680, a drop of ₹320. This ₹320 drop caused the loss percentage to increase by 4%. So 4% of CP = ₹320, meaning CP = 320/0.04 = ₹8,000. For 4% profit: SP = 8000 × 1.04 = ₹8,320. The key step is translating "4% increase in loss%" into a rupee value linked to CP.
Why this question: Split-discount problems appeared in 2024 and test whether you can track total discount in rupees versus percentages — a bookkeeping question more than a formula question.
Solving path: Total discount required = 9.5% of 48,000 = ₹4,560. Discount on first ₹28,000 at 12% = ₹3,360. Discount on next ₹12,000 at 8% = ₹960. Remaining discount = 4,560 − 3,360 − 960 = ₹240. Work entirely in rupees — do not convert back to percentages mid-way.
Why this question: The dishonest shopkeeper with false weights appears in almost every CHSL cycle. This 2023 question is a clean test of the gain% formula, and the wrong-denominator trap is live here.
Solving path: True weight = 1000 gm, false weight used = 920 gm. Error = 80 gm. Gain% = (80/920) × 100 = 8.695% ≈ 8.70%. The denominator is 920 (what the shopkeeper actually gives), not 1000 (what he claims to give). Using 1000 gives 8% — tempting but wrong.
Why this question: The "reduced SP, known profit → find profit at usual SP" pattern requires a clean chain from CP to usual SP via the given fraction. It appeared in CHSL 2023 and is a pure pattern-recognition question.
Solving path: Let CP = 100. Selling at 9/10 of usual SP gives 20% profit, so (9/10) × usual SP = 120. Usual SP = 120 × (10/9) = 133.33. Profit at usual SP = 133.33 − 100 = 33.33. Profit% = 33.33%. The fraction 9/10 is your entry point — multiply both sides by 10/9 immediately.
Calculating profit% on SP instead of CP. The percentage is always on CP unless the problem says otherwise. If a question says "profit on SP is 20%", that is a different calculation — but CHSL questions almost never state that, so default to CP as the base every time.
Applying discount to CP instead of MP. Discount is always on the marked price. If MP = ₹180 and discount = 10%, SP = ₹162, not ₹90 off CP. Confusing the base for discount is probably the single most frequent error in this chapter.
Cancelling markup and discount as if they are on the same base. A 30% markup followed by a 30% discount is not zero profit — it is a loss of 9% (since discount applies to the higher MP). Always use the net formula or set CP = 100.
Using 1000 as denominator in false-weight problems. In the gain% formula for weight manipulation, the denominator is the actual weight given (the false weight), not the stated weight. Using 1000 gives you the gain on the customer's perspective, not the shopkeeper's actual gain%.
Misreading "loss = SP of Y items" as "loss% = SP of Y items." The problem gives loss in rupees (as SP of Y items), not loss%. Compute the rupee loss first, then add to SP to get CP.
Setting up two variables when one is enough. Every CHSL profit-loss question is solvable with CP = 100 as the starting assumption. Students who introduce two unknowns (say x for CP and y for SP) spend 90+ seconds on algebra that a 20-second substitution would have handled. Commit to the CP = 100 anchor.