Profit and Loss is one of the most reliable scoring areas in RRB NTPC Quant. Questions here are formula-driven, and once you internalize the multiplier approach (more on that shortly), you will solve most questions in under 30 seconds.
Here is the core idea. Every transaction has two sides: what you paid (Cost Price / CP) and what you received (Selling Price / SP). The difference between them is either a profit or a loss.
SP > CP, it's a profit. Profit = SP - CP.SP < CP, it's a loss. Loss = CP - SP.The percentage is always calculated on CP (not SP — that trap trips up a lot of candidates):
Think of it like this: you are the shopkeeper. You paid a certain amount from your own pocket (CP). Profit or loss is measured against what came out of your pocket, not what you collected from the customer.
The Multiplier Analogy
Stop thinking in subtraction and addition — think in multipliers. A 20% profit means SP is 120% of CP, so SP = 1.2 × CP. A 25% loss means SP is 75% of CP, so SP = 0.75 × CP. This single shift — from "add/subtract" thinking to "multiply by a factor" — is what separates a 40-second solver from a 2-minute one.
Marked Price and Discount
Retailers often display a Marked Price (MP), also called the List Price. The discount is given on MP, and whatever remains after the discount is the SP. So:
A question that mixes profit-on-CP with discount-on-MP is a classic NTPC question type. You will see at least one such question per attempt.
Let's lock down the core formulas in multiplier form — you should recall these without thinking:
| Situation | Relationship |
|---|---|
| Profit of r% | SP = CP × (100 + r) / 100 |
| Loss of r% | SP = CP × (100 - r) / 100 |
| Find CP from SP + profit% | CP = SP × 100 / (100 + r) |
| Find CP from SP + loss% | CP = SP × 100 / (100 - r) |
NTPC loves questions of the form: "CP of m articles = SP of n articles. Find profit/loss%."
Here is the direct formula:
This works because you're essentially comparing what you paid for (m articles at CP) against what you sold (n articles at SP) for the same money.
Example: CP of 12 articles = SP of 10 articles.
Profit% = (12 - 10) / 10 × 100 = 20%. Done in one step.
Example: SP of 15 articles = CP of 20 articles.
Here, m = 20 (CP side), n = 15 (SP side).
Profit% = (20 - 15) / 15 × 100 = 33.33%. One step.
When a problem gives you both a discount and a profit, the link is:
Where d = discount%, p = profit%.
So: MP / CP = (100 + p) / (100 - d)
Example: 20% discount, 25% profit. Then MP/CP = 125/80 = 25/16. If CP = 960, then MP = 960 × 25/16 = 1,500. No guessing required.
When a shopkeeper sells different fractions of his stock at different profit rates, don't calculate each separately then add — use the weighted average concept:
Where w is the fraction of total cost and p is the respective profit%.
Example from the PYQ pool: 3/4 of stock at 12% profit, 1/4 at 18% profit.
Overall% = (3/4 × 12) + (1/4 × 18) = 9 + 4.5 = 13.5%. One line.
Sometimes the question says "profit equals 1/3 of CP" instead of giving a percentage. Translate immediately:
Profit = CP/3 → SP = CP + CP/3 = 4CP/3.
If SP is known, CP = SP × 3/4. This is the only form that trips people — they forget that profit-as-fraction-of-CP is just a different way to express profit%.
Pattern: "Sold at a loss of r%. What SP gives a gain of g%?"
Step 1: Find CP from loss.
Step 2: Apply gain% to CP.
Do NOT try to find a shortcut ratio between the two SPs directly — you will make sign errors. Always anchor at CP.
When you see "x% discount, y% profit", the ratio MP:CP is always (100 + y) : (100 - x). Write this ratio immediately on your rough sheet. You don't need to touch SP at all until the very end.
Worked example: 20% discount, 25% profit. Ratio = 125 : 80 = 25 : 16. CP = 960 → MP = 960 × 25/16 = 1,500.
Standard method (computing SP first, then MP): 4 steps, ~50s. This ratio method: 2 steps, ~18s.
When "CP of m articles = SP of n articles":
= (m - n)/n × 100= (n - m)/n × 100Worked example: "SP of 15 articles = CP of 20 articles." Here m = 20, n = 15. Profit% = 5/15 × 100 = 33.33%.
Standard unitary method: assign CP = 1, compute SP, subtract, divide — 5 steps, ~60s. Direct formula: 1 step, ~10s.
To find CP from SP + profit%: CP = SP × 100 / (100 + profit%). To find CP from SP + loss%: CP = SP × 100 / (100 - loss%).
Worked example: SP = 924, profit = 20%. CP = 924 × 100/120 = 924 × 5/6 = 770.
Convert 100/120 to its lowest fraction first — 5/6 — so you're multiplying 924 × 5 = 4620, then 4620 / 6 = 770. No long division.
Standard setup (let CP = x, solve 1.2x = 924): 3 steps. Fraction shortcut: 2 steps, saves ~20s.
For "fraction f₁ at profit p₁%, fraction f₂ at profit p₂%", the overall profit% is just f₁ × p₁ + f₂ × p₂ (since f₁ + f₂ = 1 and fractions are of cost, so weights are already correct).
Worked example: 3/4 at 12%, 1/4 at 18%. Overall = 0.75 × 12 + 0.25 × 18 = 9 + 4.5 = 13.5%.
Standard method (compute each lot's SP, add, find total profit): 6 arithmetic operations. Weighted average: 3 operations, ~25s saved.
When "profit = 1/n of CP", the profit% is always 100/n %. When "profit = 1/n of SP", convert first: since profit/SP = 1/n, then profit/(CP + profit) = 1/n, giving profit% = 100/(n-1) %.
Worked example: "Profit equals 1/3 of CP." Profit% = 100/3 = 33.33%. "Profit equals 1/3 of SP." Profit% = 100/(3-1) = 50%.
Standard algebraic setup: ~45s. This pattern: read-and-state in ~8s.
When you see a Profit and Loss question in the exam hall, run through this decision tree in order:
Step 1 — Identify what's given and what's asked.
Is CP given? Is SP given? Is MP + discount given? Is profit% or loss% given?
Step 2 — Is it an "articles count" problem?
If yes, apply the (m-n)/n × 100 formula directly. Skip the rest.
Step 3 — Is it a "partial lot at different profits" problem?
If yes, use weighted average f₁p₁ + f₂p₂. One line answer.
Step 4 — Is it a "find CP from SP + profit/loss%" problem?
Convert to fraction: CP = SP × 100/(100 ± r%). Reduce the fraction before multiplying.
Step 5 — Is MP involved?
Write the ratio MP:CP = (100 + profit%):(100 - discount%) immediately.
Elimination as a backup: If arithmetic gets messy, substitute the answer options back into the key formula. For a "find CP" question with four options, start with the middle option — if it's wrong, the direction of error tells you which of the remaining two to try.
Never set up a full algebraic equation for these questions — it costs 40-60 extra seconds and introduces transcription errors.
Why this question: The most basic SP-to-CP reversal. You will see this exact structure in almost every NTPC attempt. Mastering the complement multiplier here pays dividends across the entire paper.
Solving path: SP = 924, profit = 20%. Multiplier for CP: 100/120 = 5/6. CP = 924 × 5/6 = 4620/6 = 770. The key is reducing 100/120 to 5/6 before multiplying — keeps the numbers clean.
Why this question: Tests whether you reach for the weighted average shortcut or grind through full lot calculations. The shortcut saves over a minute.
Solving path: Weights are 3/4 and 1/4. Overall profit% = (3/4 × 12) + (1/4 × 18) = 9 + 4.5 = 13.5%. No need to compute individual SPs.
Why this question: The classic discount + profit combo. Every NTPC paper has at least one. The ratio method is the clean path here.
Solving path: MP:CP = (100 + 25):(100 - 20) = 125:80 = 25:16. CP = 960, so MP = 960 × 25/16 = 60 × 25 = 1,500.
Why this question: The "CP of m articles = SP of n articles" type. If you have the formula memorized, this is a 10-second question.
Solving path: m = 12, n = 10, m > n so profit. Profit% = (12-10)/10 × 100 = 2/10 × 100 = 20%.
Why this question: Same structure as above but with SP side = CP side, so the framing reverses. Watch the direction carefully.
Solving path: "SP of 15 = CP of 20" means the CP-side number (20) > SP-side number (15), so profit. m = 20, n = 15. Profit% = (20-15)/15 × 100 = 5/15 × 100 = 33.33%.
Why this question: Two-layer problem — find discount% after first computing MP and then target SP. Tests whether you anchor correctly at CP throughout.
Solving path: CP = 800. MP = 800 × 1.25 = 1,000. Target SP (5% profit) = 800 × 1.05 = 840. Discount = 1,000 - 840 = 160. Discount% = 160/1,000 × 100 = 16%.
Why this question: Profit expressed as a fraction of CP, not a percentage. Candidates who don't convert this immediately lose 90 seconds to unnecessary algebra.
Solving path: Profit = CP/3, so SP = CP + CP/3 = 4CP/3. Therefore CP = SP × 3/4 = 450 × 3/4 = 337.50.
Why this question: Two-step problem — recover CP from a loss scenario, then compute new SP for a gain. The anchor-at-CP discipline is the whole lesson.
Solving path: SP at 25% loss = 1,950. So 0.75 × CP = 1,950. CP = 1,950/0.75 = 1,950 × 4/3 = 2,600. New SP at 15% gain = 2,600 × 1.15 = 2,990.
Applying profit/loss% on SP instead of CP. The percentage always references what you paid (CP). If a question says "20% profit", it means 20% of CP — not 20% of SP. Questions sometimes phrase it ambiguously on purpose.
Confusing "SP of m = CP of n" direction. In "SP of 15 articles = CP of 20 articles", the CP side is 20 and the SP side is 15. Many candidates flip these, get Loss% = 25% instead of Profit% = 33.33%. Always identify which number is on the CP side and which is on the SP side before plugging into the formula.
Discount on CP instead of MP. Discount is always calculated on Marked Price, not Cost Price. If you see "20% discount", the base is MP, full stop.
Not reducing the complement fraction before multiplying. When computing CP = 924 × 100/120, candidates who multiply first (924 × 100 = 92,400) then divide by 120 are inviting arithmetic errors. Reduce to 5/6 first — the numbers stay manageable.
Forgetting to anchor at CP in two-step questions. In "sold at 25% loss; find SP for 15% gain", some candidates try to jump directly from the loss-SP to the gain-SP using a ratio. This fails because the two percentages have different bases. Always go back to CP first.
Treating "profit = 1/3 of CP" and "profit = 1/3 of SP" as equivalent. They are not. Profit = CP/3 gives profit% = 33.33%. Profit = SP/3 gives a different equation entirely. Read "of CP" vs "of SP" very carefully — one wrong word changes the answer by 15-20%.