Profit and Loss for competitive exam: Formulas & Tricks

If you have looked at even three previous years' SSC CGL papers, you already know this: Profit and Loss never skips an exam. It is one of the most consistent chapters in the SSC CGL Quantitative Aptitude section, and it rarely shows up alone — it hides inside Mixture and Alligation, Ratio and Proportion, Percentage, and even Data Interpretation sets. In SSC CGL Tier-1, you can expect 1–3 direct questions from this topic, and in Tier-2, which has a longer and more calculation-heavy paper, Profit and Loss questions get more twisted — combined with discounts, false weights, partnerships, and successive transactions.

The good news? Unlike Geometry or Trigonometry, Profit and Loss does not demand you memorize dozens of theorems. It rests on one simple idea: when you buy something and sell it, the difference between what you paid and what you received is either a gain in your pocket (profit) or a hole in your pocket (loss). Every formula in this chapter — no matter how complicated it looks with marked prices, discounts, or dishonest shopkeepers — is just this one idea dressed up in different situations.

In this article, we will build that understanding brick by brick: every formula explained like a teacher would explain it on a whiteboard, the "why" behind each one, the mistakes students repeatedly make, time-saving shortcuts that toppers actually use in the exam hall, and three fully solved questions ranging from basic to Tier-2 level. By the end, Profit and Loss should feel less like a formula list and more like common sense with numbers.

3. CORE CONCEPT & FORMULA GUIDE

Before the formulas, fix three terms in your head, because 90% of silly mistakes happen from mixing these up:

• Cost Price (CP) — the price at which an article is bought. This is your reference point for almost every percentage calculation in this chapter.
• Selling Price (SP) — the price at which an article is actually sold.
• Marked Price (MP) (also called List Price) — the price printed/labelled on the article, before any discount is given. MP is NOT the same as SP unless the discount is zero.

Now let's go formula by formula.

Formula 1: Profit = SP − CP

• Variables: SP = Selling Price, CP = Cost Price.
• Why it works: If you sold something for more than you paid, whatever is "extra" in your hand after the sale is your profit. It's pocket-money logic — nothing more.
• Common mistake: Students sometimes subtract in the wrong order under exam pressure (CP − SP) and get a negative profit without realising it actually means a loss. Always check: if SP > CP, it's profit; if this formula gives you a negative number, you're actually looking at a loss.

Formula 2: Loss = CP − SP

• Variables: CP = Cost Price, SP = Selling Price.
• Why it works: This is simply Formula 1 flipped, applied only when CP > SP — you spent more than you got back, so the difference is money lost.
• Common mistake: Applying both Profit and Loss formulas to the same question and getting confused about which one to report. Rule of thumb: compare CP and SP first, decide profit or loss, then apply only the relevant formula.

Formula 3: Profit % = (Profit / CP) × 100

• Variables: Profit (in rupees), CP = Cost Price.
• Why it works: Profit percentage always measures gain relative to what you invested (CP), not relative to what you received (SP). This is the single most important rule in the entire chapter.
• Common mistake: Calculating Profit % using SP in the denominator instead of CP. This is the #1 error SSC CGL aspirants make — always divide by CP unless a question explicitly says "profit percent on selling price."

Formula 4: Loss % = (Loss / CP) × 100

• Variables: Loss (in rupees), CP = Cost Price.
• Why it works: Same logic as Profit % — loss is also measured against your original investment, the CP.
• Common mistake: Forgetting that loss percentage, like profit percentage, is always based on CP, not on MP or SP.

Formula 5 & 6: SP = CP × (100 + P%)/100 and SP = CP × (100 − L%)/100

• Variables: CP = Cost Price, P% = Profit percent, L% = Loss percent.
• Why it works: This is just Formula 3/4 rearranged to solve for SP directly. If CP is treated as "100 units," a profit of P% means SP is "100 + P" units; a loss of L% means SP is "100 − L" units. This is exactly why the Ratio Method (explained in Section 4) works so beautifully.
• Common mistake: Using (100 − P%) when there's a profit, or (100 + L%) when there's a loss — a simple sign confusion that costs easy marks.

Formula 7 & 8: CP = SP × 100/(100 + P%) and CP = SP × 100/(100 − L%)

• Variables: SP = Selling Price, P% = Profit percent, L% = Loss percent.
• Why it works: These are Formulas 5 and 6 solved for CP instead of SP. Useful whenever a question gives you the selling price and the profit/loss percentage and asks you to find what the item originally cost.
• Common mistake: Cross-multiplying incorrectly and accidentally swapping CP and SP formulas — always double check by asking "am I solving for what was paid (CP) or what was received (SP)?"

Formula 9: Discount = MP − SP, and Discount % = (Discount / MP) × 100

• Variables: MP = Marked Price, SP = Selling Price.
• Why it works: A discount is a reduction from the marked (labelled) price to arrive at the actual selling price. It is always calculated as a percentage of the Marked Price, never of the Cost Price.
• Common mistake: Calculating discount percentage on CP instead of MP — this is the second most common conceptual error in this chapter, right after the Profit%-on-SP mistake.

Formula 10: SP = MP × (100 − D%)/100

• Variables: MP = Marked Price, D% = Discount percent.
• Why it works: Same "100 units" logic as before — if MP is 100 units and a discount of D% is given, the buyer only pays (100 − D) units.
• Common mistake: Forgetting that MP and CP are two completely different quantities. A shopkeeper can mark an item well above CP specifically to "absorb" a discount and still make a profit — students often assume MP = CP by mistake.

Formula 11: Equivalent Single Discount for Successive Discounts

Single Discount % = D1 + D2 − (D1 × D2)/100

• Variables: D1, D2 = the two successive discount percentages.
• Why it works: If you apply two discounts one after another, the second discount is calculated on an already-reduced price, not on the original MP. So simply adding D1 + D2 overstates the real discount. The formula corrects for this "discount on discount" overlap by subtracting (D1×D2)/100.
• Common mistake: Simply adding two successive discounts (e.g., treating "20% and 10% off" as a flat 30% off) — this is one of the most exploited traps in SSC CGL questions and always leads to a wrong answer that "looks right."

Formula 12: Equal Selling Price, Equal Profit% and Loss% → Always a Net Loss

Net Loss % = (Common %)² / 100

• Variables: Common % = the profit percentage on one article, which equals the loss percentage on the other.
• Why it works: When two articles are sold at the same SP, one at x% profit and the other at x% loss, their cost prices are actually different — the article sold at a loss had a higher CP than the one sold at profit, because a bigger original cost is required to still result in the same SP after subtracting a loss. This asymmetry always results in an overall loss, never a profit or a break-even, regardless of what x is.
• Common mistake: Assuming profit and loss "cancel out" to give no gain, no loss. They never fully cancel — there is always a net loss.

Formula 13: Dishonest Dealer Using False Weights (selling at cost price, but with less quantity)

Profit % = [(True Weight − False Weight) / False Weight] × 100

Teacher's Breakdown:

• Variables: True Weight = the weight that should actually be given (usually 1000 g), False Weight = the reduced weight actually given.
• Why it works: A dealer who claims "no profit, no loss" but hands over less quantity than promised is effectively charging the price of 1000 g while only spending on (say) 800 g worth of goods. The "missing" 200 g is pure profit — hence you compare the shortfall to what was actually given away (False Weight), not to the full 1000 g.
• Common mistake: Dividing the error by the True Weight (1000 g) instead of the False Weight — remember, profit is always measured against what was actually invested/given, not the promised amount.

Formula 14: Combined Markup + False Weight

Overall Profit % = [(100 + Markup%) × (True Weight / False Weight)] − 100

• Variables: Markup% = percentage by which price is marked above CP, True Weight and False Weight as before.
• Why it works: This formula simply chains two profit-generating tricks together — marking the price up and shortchanging the weight — using the same "100 units" ratio logic from Formulas 5–8. You are essentially finding the combined effect of two independent multipliers.
• Common mistake: Adding the markup % and the weight-shortfall % directly (Markup% + Shortfall%) instead of combining them multiplicatively. Just like successive discounts, these two effects compound — they don't simply add up.

4. SHORTCUT TRICKS & ALTERNATIVE METHODS

Trick 1: The Ratio Method (fastest for pure Profit/Loss % questions)

Whenever you're given a profit or loss percentage, instantly convert it into a CP : SP ratio:

• Profit of P% → CP : SP = 100 : (100 + P)
• Loss of L% → CP : SP = (100 − L) : 100

When to use it: Any question where you're given one value (CP or SP) and a percentage, and asked to find the other — or where two scenarios need to be compared. Instead of writing an equation and solving algebraically, you scale the ratio directly, which is much faster under time pressure.

When to stick to the basic formula: If the question involves three or more linked transactions (e.g., A sells to B at a profit, B sells to C at a loss), a direct formula chain is often clearer than juggling multiple ratios at once — use the ratio method for single-step problems and the formula method for multi-step chains.

Trick 2: The "Error/Difference" Method for Successive Discounts & False Weight

Instead of applying the full successive-discount formula every time, use quick multiplication of "retained fractions":

• A discount of D% means the buyer retains (100 − D)% of the price.
• For two successive discounts, multiply the retained fractions: Final Price = MP × [(100−D1)/100] × [(100−D2)/100]

When to use it: When you need the final price directly rather than the equivalent single discount percentage — it's one less step than finding the combined discount % first.

When to stick to the basic formula: If the question specifically asks for the "equivalent single discount," compute Formula 11 directly rather than reverse-engineering it from the final price — it avoids an extra subtraction step and possible rounding errors.

Trick 3: The "Equal Profit-Loss %" Shortcut for Two Articles Sold at Same SP

Memorize this outright: if two items are sold at the same SP, one at x% profit and the other at x% loss, the seller always incurs a net loss of (x/10)² percent. For example, x = 20% → net loss = (20/10)² = 4%. x = 10% → net loss = 1%.

When to use it: The instant you spot "sold at the same price," "one at a gain of x%, the other at a loss of x%" — this is a direct plug-in, no algebra required.

When to stick to the basic formula: If the two profit/loss percentages are different (not equal), this shortcut does not apply — you must set up individual CP equations using Formulas 7 and 8 and solve normally.

5. STEP-BY-STEP EXAMPLES

Type 1: Basic/Direct Formula Application

Question: A shopkeeper bought a fan for ₹800 and sold it for ₹920. Find his profit percentage.

Detailed Step-by-Step Solution:

1. CP = ₹800, SP = ₹920. Since SP > CP, there is a profit.
2. Profit = SP − CP = 920 − 800 = ₹120 (Formula 1)
3. Profit % = (Profit / CP) × 100 = (120 / 800) × 100 (Formula 3)
4. Profit % = 15%

Shortcut Solution: Using the Ratio Method in reverse: the difference (SP − CP = 120) as a fraction of CP (800) directly gives 120/800 = 3/20 = 15%. No separate "profit" line needed — just compute the fraction and convert to a percentage in one line.

Type 2: Moderate/Twisted Question

Question: A trader marks his goods 40% above the cost price and then allows a discount of 15% on the marked price for cash payment. Find his profit percentage.

Detailed Step-by-Step Solution:

1. Let CP = ₹100 (always assume CP = 100 when only percentages are given — it makes the arithmetic clean).
2. Marked Price = CP + 40% of CP = 100 + 40 = ₹140 (Formula: MP = CP × (100+Markup%)/100)
3. Discount = 15% of MP = 15% of 140 = ₹21
4. SP = MP − Discount = 140 − 21 = ₹119 (Formula 9)
5. Profit = SP − CP = 119 − 100 = ₹19
6. Profit % = (19/100) × 100 = 19%

Shortcut Solution: Chain the two "retained/added fractions" directly without finding MP and Discount separately: SP = CP × (140/100) × (85/100) = 100 × 1.4 × 0.85 = ₹119 Profit % = SP − CP (when CP = 100) read off directly = 19%. This "multiply the multipliers" approach (1.40 × 0.85 = 1.19 → 19% profit) is the fastest way to handle any markup-then-discount question in one line.

Type 3: Advanced/Previous Year SSC CGL Tier-2 Level Question

Question: A dishonest shopkeeper marks his goods 20% above the cost price, but while selling, uses a weight that is 20% less than what he claims (i.e., he gives only 800 g when he charges for 1000 g). Find his overall profit percentage.

Detailed Step-by-Step Solution:

1. Let the true cost price of 1000 g of goods = ₹100, so CP per gram = ₹0.1.
2. Marked Price for 1000 g = CP + 20% of CP = 100 + 20 = ₹120. This is the price the shopkeeper charges for what he claims is 1000 g.
3. But he actually hands over only 800 g. The cost of this 800 g to the shopkeeper = 800 × ₹0.1 = ₹80.
4. So, for a cost of ₹80, the shopkeeper receives ₹120 (the marked price for the falsely-labelled "1000 g").
5. Profit = SP − CP = 120 − 80 = ₹40
6. Profit % = (40/80) × 100 = 50%

Shortcut Solution: Use Formula 14 directly: Overall Profit % = [(100 + Markup%) × (True Weight/False Weight)] − 100 = [(100 + 20) × (1000/800)] − 100 = [120 × 1.25] − 100 = 150 − 100 = 50%

This one-line substitution is exactly why memorizing Formula 14 (rather than re-deriving it every time) is worth the effort — Tier-2 papers frequently disguise this exact setup with different numbers, and recognizing the pattern instantly saves 2–3 minutes per question.

COASPIRANT ADVICE

Profit and Loss rewards students who understand why a formula works rather than those who simply memorize it — because SSC CGL loves to disguise the same core idea (CP vs. SP, in "100 units" terms) inside marked prices, discounts, dishonest dealers, and partnerships. Once you internalize that everything in this chapter is measured relative to CP, and that percentages compound rather than add when transactions are chained together, most "tricky" questions stop feeling tricky.

Pro-tip for revision: Keep a single-page formula sheet with just the 14 formulas above, written in your own handwriting, and solve 10 mixed-type questions from it every alternate day rather than 50 questions once a week — spaced repetition on a chapter like this builds the pattern-recognition speed that actually wins marks in the exam hall, far more than binge-solving does.