Profit and loss is, at its core, the arithmetic of trade — comparing what something costs you versus what you receive for it. Every transaction in this chapter comes down to three numbers: Cost Price (CP), Selling Price (SP), and the difference between them.
Here is the plain-language version: CP is what you pay to acquire the article (including any overhead — repairs, transport, taxes). SP is what the buyer hands you. If SP exceeds CP, the excess is profit. If SP is below CP, the deficit is loss. Percentage profit or loss is always calculated on CP, not SP — this single fact is responsible for more wrong answers in AFCAT mocks than almost anything else in arithmetic.
Beyond the basic pair, AFCAT questions introduce a third price: the Marked Price (MP), also called the List Price. Think of it as the tag on the shelf — the aspirational price the shopkeeper displays. A discount is a reduction given on MP. The actual transaction happens at SP, which is MP × (1 - discount%). The shopkeeper's game is to mark MP high enough that even after offering a discount, SP still exceeds CP.
A good analogy: imagine a bazaar vendor. He buys mangoes at wholesale (CP), writes a price tag on the crate (MP), shouts "special discount today" (discount), and you pay what you negotiate (SP). The vendor's profit depends on the gap between his wholesale cost and your final payment — the tag and the discount are just theatre to manage that gap.
Where AFCAT gets interesting is in the faulty weight variant — the shopkeeper quotes the correct per-kg price but physically cheats on the scale. There is also the batch-rate variant (buy at x for Rs. A, sell at y for Rs. B). These both reduce to the same framework once you find the per-unit CP and SP. Recognise the variant in the first reading of the question, and half the work is done.
The multiplier form — using (100 + P%)/100 — is faster than the two-step "find profit, add to CP" method. Internalise it.
When a question gives you two of the three values {markup%, discount%, net gain/loss%}, you can derive the third. The relationship is:
Combine them:
In AFCAT PYQs, this triangle appears in one of two forms:
Assume CP = 100, compute MP and SP, and read off the answer. This base-100 trick eliminates fractions in most cases.
When a dealer sells at cost price but uses a short weight:
Look — the denominator is the false weight (what he actually gives), not the true weight. This is intuitive once you see it: he sells 800g but collects money for 1000g, so his effective CP for what he sold is based on 800g.
For the 800g / 1000g case: (1000 - 800) / 800 × 100 = 200/800 × 100 = 25%. Match it against the PYQ below.
Given: buy at m items for Rs. A, sell at n items for Rs. B.
Per-unit CP = A/m. Per-unit SP = B/n.
For the oranges PYQ (buy 5 for Rs. 4, sell 4 for Rs. 5): CP per unit = 0.80, SP per unit = 1.25. Gain% = (1.25 - 0.80)/0.80 × 100 = 56.25%. Don't rush — the numbers feel "similar" but are inverted.
"CP of x articles = SP of y articles" — this type appears repeatedly. The interpretation: you buy x articles, each costing 1 unit, total CP = x. Those x articles, when all sold individually at this SP, generate revenue of x for only y of them. So SP per article = x/y.
For "CP of 12 pens = SP of 10 pens": gain% = (12 - 10)/10 × 100 = 20%. This is a three-second calculation once you know the formula.
These questions test whether you can set up the algebra quickly. Let CP = C, original SP = S.
Original profit = S - C. New SP = 2S, new profit = 2S - C.
The constraint "profit triples" gives: 2S - C = 3(S - C) → 2S - C = 3S - 3C → 2C = S.
So original profit = S - C = 2C - C = C. Profit% = (C/C) × 100 = 100%.
The pattern to notice: whenever the question says "SP changes by factor k, profit changes by factor m," set up one equation with two unknowns (CP and original SP), and the constraint collapses it to a single unknown.
Whenever you see CP + markup% + discount% in the same question, set CP = 100 immediately. Don't introduce variables. MP = 100 + markup%. SP = MP × (1 - discount%). Read gain/loss directly as the numeric gap between SP and 100. Standard algebraic method: ~60s. Base-100 substitution: ~20s. The 12 pens / 10 pens type and the oranges type don't benefit from this — use the quantity-ratio formula there instead.
Profit% on faulty weight = (True − False) / False × 100. The mnemonic: the shopkeeper's cost is based on what he actually gives (False), not what you think you bought (True). Standard algebraic approach (finding CP and SP separately): 4 steps. Direct formula: 1 step. For 800g sold as 1 kg: (1000 − 800)/800 × 100 = 25% in under 10 seconds.
"CP of x articles = SP of y articles" always resolves to gain% = (x − y)/y × 100. No need to assign a per-unit price. Just plug x and y. Works only when x > y (profit). If y > x, it is a loss: (y − x)/y × 100. Verifying with full calculation: 3 steps. Direct formula: 1 step. Saves one full multiplication in the exam hall.
When a question says "sold at P% profit / Q% loss, difference in SP is Rs. D," use: CP = D / (P + Q) × 100. Here (P + Q) = total percentage swing between the two scenarios. For the PYQ below: P = 7, Q = 12, D = 195. CP = 195/19 × 100 = Rs. 1025. Standard setup-and-solve: 5 algebraic steps. Direct formula: 2 arithmetic steps.
Any money spent before the sale — repair, transport, packaging — is part of CP. Do not add it to profit. Eliminate options that are calculated on purchase price alone when the question mentions additional expenses. Takes you from 4 options to 1 or 2 immediately. Eliminates the most common calculation shortcut that the question-setter deliberately plants.
Read the question and classify it in the first five seconds:
Step 1 — Identify what type:
(True − False)/False × 100 directly.(x − y)/y × 100 directly.D/(P + Q) × 100.Step 2 — Assign base value: CP = 100 unless the question gives a concrete CP — in that case, work with the actual number directly.
Step 3 — Never work backwards from SP to CP using SP as the base. That gives a different percentage and is the primary trap in AFCAT options.
Step 4 — In multi-step questions, finish every intermediate value before attempting the final calculation. Do not carry symbolic fractions into arithmetic — convert to decimals at each step.
If you cannot classify in five seconds, pick the most-mark-up type (MP-Discount-Gain) and see if the numbers fit. That is the most frequent AFCAT variant.
Why this question: The classic MP-Discount-Gain triangle where all three values are constrained. AFCAT sets this up with clean numbers that make direct algebraic solving fast — but base-100 is faster.
Solving path: CP = 2000, gain = 5%, so SP = 2000 × 1.05 = 2100. MP gives SP after 16% discount: SP = MP × 0.84 = 2100. Therefore MP = 2100 / 0.84 = 2500. Answer: Rs. 2500. One thing to watch — discount is on MP, not on CP. Don't mix them.
Why this question: The two-SP-difference type. The key is recognising that the Rs. 195 gap corresponds to a 19% swing in CP (7% + 12%). This is a direct formula opportunity — do not set up full algebraic expressions.
Solving path: Difference in SP = 1.07x − 0.88x = 0.19x = 195. So x = 195/0.19 = 1025. The fraction 195/0.19 = 19500/19 = 1025. Verify: 0.19 × 1000 = 190, 0.19 × 1025 = 194.75 ≈ 195. Confirm: Rs. 1025.
Why this question: Markup and discount given, find net discount%. The base-100 method is exact here and takes under 20 seconds.
Solving path: CP = 100, MP = 140 (40% markup). Gain = 12%, so SP = 112. Discount = MP − SP = 140 − 112 = 28. Discount% = 28/140 × 100 = 20%. The wrong-answer trap here is calculating discount% on CP (28/100 = 28%) — that is option (c), planted deliberately.
Why this question: Tests whether you can set up the doubled-SP / tripled-profit equation without panicking. It is a purer algebra exercise than most profit questions, and AFCAT uses it to separate well-prepared candidates.
Solving path: Let CP = C, original SP = S, profit = S − C. New SP = 2S, new profit = 2S − C. Condition: 2S − C = 3(S − C) = 3S − 3C. Rearranging: 2C = S. Original profit = S − C = 2C − C = C. Profit% = C/C × 100 = 100%.
Why this question: The faulty-weight variant — the shopkeeper gives 800g but charges for 1000g. The formula (True − False)/False × 100 resolves this in one step.
Solving path: True weight = 1000g, false weight = 800g. Profit% = (1000 − 800)/800 × 100 = 200/800 × 100 = 25%. The trap: using 1000 in the denominator instead of 800, giving 20% — option (b), a distractor for candidates who get the numerator right but the denominator wrong.
Why this question: Batch-rate problem — rates are given as "x items for Rs. y," not per item. Find per-unit CP and SP, then compute gain.
Solving path: CP per orange = 4/5 = 0.80. SP per orange = 5/4 = 1.25. Gain% = (1.25 − 0.80)/0.80 × 100 = 0.45/0.80 × 100 = 56.25%. Note how the rates are intentionally swapped (5 for Rs. 4 vs 4 for Rs. 5) — read both numbers carefully before assigning CP and SP.
Calculating profit% on SP instead of CP. This is the single most common source of wrong answers. If you get a percentage answer that looks "almost right" but is slightly lower than the correct option, you've likely divided by SP. Always divide by CP.
Ignoring overhead costs in CP. When a question says "bought for Rs. 800 and spent Rs. 200 on repair," the CP is Rs. 1000. Applying 20% profit on Rs. 800 alone gives Rs. 960 — a distractor that appears as an option.
Using True weight in the denominator for faulty-weight questions. The denominator must be the false weight (what the customer actually received). Using true weight gives 20% instead of 25% for the 800g/1000g case.
Applying discount% on CP instead of MP. Discount is always on Marked Price. If a question says "15% discount" and you apply it to CP, you get a different SP and a different (wrong) profit%.
In batch-rate questions, confusing which rate is buy and which is sell. "Buys 5 for Rs. 4, sells 4 for Rs. 5" — the lower denominator (selling 4) gives a higher per-unit SP. Reverse them mentally and you get a loss instead of a gain.
Treating "profit triples" as "SP triples." In the doubled-SP scenario, it is the profit that triples, not the SP. Setting up 2S = 3S instead of 2S − C = 3(S − C) gives CP = 0, which is obviously wrong — but in exam pressure, it is a tempting shortcut.