If you have ever bought something to resell it — load, snacks, ukay-ukay finds, or goods in a sari-sari store — you already understand the heart of this topic. You buy at one price and sell at another, and the difference is your profit or your loss. Profit and loss is one of the most practical, real-money topics on the Civil Service Exam, and it rewards a very small set of ideas applied carefully. Let's make those ideas rock-solid.
Profit-and-loss questions describe buying and selling. They give you some of the prices involved and ask you to find a missing one — the cost, the selling price, or the percentage gained or lost. Everything rests on three quantities (cost price, selling price, and profit/loss) and one golden rule about which price the percentage is measured against.
On the Civil Service Exam, profit and loss is a reliable part of Numerical Reasoning, and it leans directly on the Percentage lesson — every profit or loss is ultimately a percentage of something. Counting the questions that fold in discounts and mark-ups, this topic touches 4 to 7 items on a typical exam.
The difficulty is intermediate. The arithmetic is simple; the exam is really checking whether you measure the percentage against the cost price (not the selling price), and whether you can keep "marked price," "cost price," and "selling price" straight. Nail those and this becomes easy, dependable marks.
After completing this lesson you will be able to:
You should be comfortable with:
Quick refresher on the prerequisite that matters most: multiplier thinking. To increase a value by 20%, multiply by 1.20; to decrease by 20%, multiply by 0.80; to reverse a change, divide by the multiplier. All of profit and loss is built on this. If that feels shaky, review the Percentage lesson first — it will make this entire chapter effortless.
Profit and loss is the math of business and shopping, which touches almost everyone in the Philippines:
Knowing profit and loss means you can never be fooled by a clever price tag again — and that is a life skill the exam happens to test.
We build from the three prices up to the trickiest exam patterns.
Analogy: Think of CP as the money that leaves your pocket to buy the goods, and SP as the money that comes back when you sell. If more comes back than left, that's profit; if less comes back, that's loss. The tag price (MP) is just what you hope to sell at before any discount.
Profit % and Loss % are always calculated on the Cost Price, unless a problem explicitly says otherwise.
Profit % = (Profit ÷ CP) × 100 Loss % = (Loss ÷ CP) × 100
A vendor buys a bag for ₱200 and sells it for ₱250. Profit = 250 − 200 = ₱50. Profit % = 50 ÷ 200 × 100 = 25%.
Why the cost, not the selling price? Because profit is your return on what you invested, and what you invested is the cost. Measuring against the selling price would flatter the numbers and isn't the convention. This one rule is the most-tested idea in the whole topic — burn it in.
Just like percentage increase, you can jump straight to the selling price:
SP = CP × (1 + Profit%) for a profit, or SP = CP × (1 − Loss%) for a loss.
A shopkeeper buys an item for ₱800 and wants a 15% profit. SP = 800 × 1.15 = ₱920. If instead he sells at a 10% loss: SP = 800 × 0.90 = ₱720.
When you're given the selling price and the profit or loss percent, divide to recover the cost (the reverse-percentage idea).
CP = SP ÷ (1 + Profit%) for a profit, or CP = SP ÷ (1 − Loss%) for a loss.
An item is sold for ₱360 at a 20% profit. CP = 360 ÷ 1.20 = ₱300. An item is sold for ₱720 at a 10% loss. CP = 720 ÷ 0.90 = ₱800.
Common trap: to undo a 20% profit, students multiply 360 × 0.80. That's wrong — you must divide by 1.20. Reversing a change means dividing by the multiplier, never multiplying by a "matching" percent.
A discount is a percentage off the marked price (not the cost). So:
Selling Price = Marked Price × (1 − Discount%).
A jacket is marked ₱1,500 and sold at a 20% discount. SP = 1,500 × 0.80 = ₱1,200.
Discounts and profit are taken from different bases — discount from the marked price, profit from the cost price. Confusing the two is a classic error. A single problem can involve both: a shopkeeper marks goods above cost, then gives a discount, and you find the resulting profit.
A trader marks goods 40% above cost, then allows a 10% discount. Find the profit percent. Let CP = ₱100. Then MP = 140. SP = 140 × 0.90 = ₱126. Profit = 26, so profit % = 26% (not 30%).
Two discounts in a row do not simply add — the second is taken from the already-reduced price (exactly like successive percentage changes).
A ₱1,000 item gets 10% off, then another 10% off the reduced price. After first: 1,000 × 0.90 = ₱900. After second: 900 × 0.90 = ₱810. The combined discount is 19%, not 20%.
A recurring exam pattern: a seller claims to sell "at cost price" but secretly gives less weight than paid for, creating hidden profit.
A dealer claims to sell rice at cost but uses a 900-gram weight for every advertised kilogram (1,000 g). What is the real profit percent? The dealer receives payment for 1,000 g of cost but only hands over 900 g. Profit is measured on the cost actually given: Profit % = (shortage ÷ actual weight given) × 100 = (100 ÷ 900) × 100 ≈ 11.1%.
The key is dividing the shortage by the actual weight given (900), because that is the true cost basis — not the claimed 1,000.
Another favorite: two items sold at the same selling price, one at x% profit and the other at x% loss. The overall result is always a loss, of exactly (x ÷ 10)² percent.
Two watches are each sold for ₱1,200; one at 20% profit, the other at 20% loss. Overall? First watch: CP = 1,200 ÷ 1.20 = ₱1,000. Second: CP = 1,200 ÷ 0.80 = ₱1,500. Total cost ₱2,500, total sale ₱2,400 → loss ₱100 → loss % = 100 ÷ 2,500 = 4% = (20 ÷ 10)². The shortcut matches.
When several people invest together — a common set-up for a sari-sari store or a small buy-and-sell venture — the profit is shared in the ratio of their investments, and if they invested for different lengths of time, in the ratio of investment × time (called "capital-months").
Aling Rosa puts in ₱30,000 for the full 12 months; Mang Tonyo puts in ₱40,000 but only for the last 6 months. Their sharing ratio is 30,000 × 12 : 40,000 × 6 = 360,000 : 240,000 = 3 : 2.
If the profit is ₱25,000, that splits into 3 + 2 = 5 shares of ₱5,000 each: Rosa gets ₱15,000, Tonyo ₱10,000. Partnership problems are really ratio problems wearing a business costume — money in and time in both count.
Break-even is the point where selling price exactly equals cost — no profit, no loss. It's the reference line for pricing: sell above break-even to profit, below it to lose. Recognizing "break-even" in a question tells you SP = CP, which often unlocks the setup immediately.
With the concepts secured, let's picture, tabulate, and drill.
| Formula | Meaning |
|---|---|
| Profit = SP − CP | Gain on a sale |
| Loss = CP − SP | Shortfall on a sale |
| Profit % = (Profit ÷ CP) × 100 | Gain as a percent of cost |
| Loss % = (Loss ÷ CP) × 100 | Loss as a percent of cost |
| SP = CP × (1 + Profit%) | Selling price for a target profit |
| SP = CP × (1 − Loss%) | Selling price at a loss |
| CP = SP ÷ (1 + Profit%) | Recover cost from a profit sale |
| CP = SP ÷ (1 − Loss%) | Recover cost from a loss sale |
| SP = MP × (1 − Discount%) | Price after a discount |
| Two discounts a%, b% | net = a + b − (a·b ÷ 100) |
| False weight profit % | (shortage ÷ actual weight given) × 100 |
| Same SP, ±x% | overall loss of (x ÷ 10)² % |
Note on the two-discount formula: it's the successive-percentage-change formula with both changes negative, which simplifies to a + b − ab/100. For 10% and 10%: 10 + 10 − 1 = 19% off.
| When the problem says… | Recognize… |
|---|---|
| "bought for… sold for…" | compute Profit = SP − CP, then % on CP |
| "gain/profit of X%" | SP = CP × (1 + X%) |
| "loss of X%" | SP = CP × (1 − X%) |
| "sold for… at a profit/loss of X%, find cost" | CP = SP ÷ (1 ± X%) — divide! |
| "marked price… discount…" | SP = MP × (1 − discount) |
| "marks up… then discount…" | mark-up on CP, discount on MP; find profit on CP |
| "two successive discounts" | don't add; a + b − ab/100 |
| "uses a false/short weight" | (shortage ÷ actual given) × 100 |
| "both sold at the same price, one profit one loss" | overall loss (x/10)² % |
Step 1 — Identify which prices are given (CP, SP, MP) and which is unknown. ↓ Step 2 — Identify the base of every percentage. Profit/loss → CP; discount → MP. Label them. ↓ Step 3 — Choose the direction. Going from cost to selling price → multiply. Going from selling price back to cost → divide. ↓ Step 4 — Compute using the multiplier form; keep pesos attached. ↓ Step 5 — Sanity-check. A profit means SP > CP; a loss means SP < CP; a discounted price is below the marked price. If your numbers violate this, you swapped a base.
Why Step 2 matters most: picking the wrong base (selling price instead of cost, or cost instead of marked price) is the defining mistake of this topic. Always label the base before you compute.
Example 1. A vendor buys a toy for ₱150 and sells it for ₱180. Find the profit and the profit percent. Solution: Profit = 180 − 150 = ₱30. Profit % = 30 ÷ 150 × 100 = 20%. Difficulty: ★☆☆☆☆
Example 2. An item costing ₱500 is sold for ₱450. Find the loss percent. Solution: Loss = 500 − 450 = ₱50. Loss % = 50 ÷ 500 × 100 = 10%. Difficulty: ★☆☆☆☆
Example 3 (find SP). A trader buys goods for ₱1,200 and wants a 25% profit. What selling price achieves this? Solution: SP = 1,200 × 1.25 = ₱1,500. Difficulty: ★★☆☆☆
Example 4 (find CP — reverse). An appliance is sold for ₱6,900 at a 15% profit. What did it cost the seller? Solution: CP = 6,900 ÷ 1.15 = ₱6,000. Check: 6,000 × 1.15 = 6,900. ✓ Common mistake: computing 6,900 × 0.85 = 5,865 — wrong; you must divide by 1.15. Difficulty: ★★★☆☆
Example 5 (bulk buying). A store buys 20 pens for ₱300 and sells them at ₱18 each. Find the profit percent. Thinking: Total cost ₱300; total revenue 20 × 18. Solution: SP total = ₱360. Profit = 60. Profit % = 60 ÷ 300 × 100 = 20%. Difficulty: ★★☆☆☆
Example 6 (mark-up then discount). A shopkeeper marks goods 40% above cost, then gives a 10% discount at the counter. What is the profit percent? Thinking: Work with CP = ₱100 for ease. Solution: MP = 140; SP = 140 × 0.90 = ₱126; profit = 26 → 26% profit. Difficulty: ★★★☆☆
Example 7 (successive discounts). A ₱2,000 gadget is offered at 20% off, then a further 10% off for members. What is the final price, and the single equivalent discount? Solution: 2,000 × 0.80 = 1,600; 1,600 × 0.90 = ₱1,440. Single equivalent discount: 0.80 × 0.90 = 0.72, so 28% off (not 30%). Check: 2,000 × 0.72 = 1,440. ✓ Difficulty: ★★★☆☆
Example 8 (change the target profit). By selling a radio for ₱90, a dealer loses 10%. What price should he sell it for to gain 20%? Thinking: First recover the cost, then apply the new target. Solution: CP = 90 ÷ 0.90 = ₱100. For a 20% gain: SP = 100 × 1.20 = ₱120. Difficulty: ★★★★☆
Example 9 (false weight). A grocer sells rice "at cost" but uses an 800-gram weight in place of a kilogram. What is the real profit percent? Thinking: He collects the price of 1,000 g but delivers only 800 g; profit is on the 800 g actually given. Solution: shortage = 200 g. Profit % = 200 ÷ 800 × 100 = 25%. Difficulty: ★★★★☆
Example 10 (two articles, same SP). Two phones are each sold for ₱4,800. One is sold at a 20% profit, the other at a 20% loss. What is the overall result? Solution: First CP = 4,800 ÷ 1.20 = ₱4,000; second CP = 4,800 ÷ 0.80 = ₱6,000. Total cost ₱10,000, total sale ₱9,600 → loss ₱400 → 4% loss (matching (20 ÷ 10)²). Difficulty: ★★★★★
Example 11 (discount and profit together). A cabinet is marked ₱5,000 and sold at a 12% discount. If the cost price was ₱3,850, what is the profit percent (to the nearest whole number)? Thinking: Find SP from the marked price, then measure profit on the cost. Solution: SP = 5,000 × 0.88 = ₱4,400. Profit = 4,400 − 3,850 = ₱550. Profit % = 550 ÷ 3,850 × 100 ≈ 14%. Difficulty: ★★★★☆
Example 12 (find the marked price). A shopkeeper wants a 25% profit on an item costing ₱400 after giving a 20% discount on the marked price. What should the marked price be? Thinking: Work backward: required SP first, then the MP that yields it after discount. Solution: Required SP = 400 × 1.25 = ₱500. Since SP = MP × 0.80, MP = 500 ÷ 0.80 = ₱625. Check: 625 × 0.80 = 500, and 500 is 25% above 400. ✓ Difficulty: ★★★★★
Example 13 (partnership). Ben invests ₱50,000 and Cita invests ₱75,000 in a buy-and-sell business for the same period. They earn ₱40,000 profit. How much is Ben's share? Thinking: Same period → share in the ratio of investments: 50,000 : 75,000 = 2 : 3. Solution: 5 shares; one share = 40,000 ÷ 5 = ₱8,000. Ben (2 shares) = ₱16,000 (Cita ₱24,000). Check: 16,000 + 24,000 = 40,000. ✓ Difficulty: ★★★★☆
Example 14 (partnership with time). Dan invests ₱20,000 for 12 months and Ella invests ₱30,000 for 8 months. If the profit is ₱44,000, find each partner's share. Thinking: Use capital-months: 20,000 × 12 : 30,000 × 8 = 240,000 : 240,000 = 1 : 1. Solution: Equal ratio → each gets ₱22,000. Insight: Ella invested more money but for less time; the two effects exactly cancel, so they split evenly. This is why time matters, not just the amount. Difficulty: ★★★★★
Example 15 (loss then required price). A merchant buys cloth for ₱600 and sells it at a 5% loss. To break even instead, what should the selling price have been, and what was the actual selling price? Solution: Actual SP = 600 × 0.95 = ₱570 (the 5% loss). Break-even price = the cost itself = ₱600; actual SP was ₱570. Difficulty: ★★★☆☆
Profit and loss runs on three prices — Cost (CP), Selling (SP), and Marked (MP) — and one golden rule: profit and loss percentages are measured on the cost. Move forward from cost to selling price by multiplying (× (1 + profit%)) and backward from selling price to cost by dividing. Discounts are taken from the marked price, and successive discounts compound rather than add. Recognize the exam's favorite set-pieces — mark-up-then-discount, false weights ((shortage ÷ actual given) × 100), and two articles at the same price (a guaranteed (x/10)² % loss). Above all, label the base of every percentage before you compute, and check that profit means SP > CP. Do that, and this is one of the friendliest scoring topics on the exam.
| Topic | Key point |
|---|---|
| Profit / Loss | SP − CP / CP − SP |
| Profit % / Loss % | on the COST price |
| Cost → price | multiply by (1 ± %) |
| Price → cost | divide by (1 ± %) |
| Discount | on the MARKED price |
| Two discounts | a + b − ab/100 (compound) |
| False weight | shortage ÷ actual weight given × 100 |
| Same SP, ±x% | overall loss (x/10)² % |
| Direction check | profit → SP > CP; loss → SP < CP |
Why is profit measured on the cost, not the selling price? Because profit is the return on what you put in, and what you put in is the cost. It's the standard convention; unless a question explicitly says "profit on selling price," use the cost.
How do I reverse a profit to find the cost? Divide, don't subtract. If SP is ₱360 at 20% profit, CP = 360 ÷ 1.20 = ₱300. Multiplying 360 by 0.80 gives the wrong answer.
Are discount and profit the same thing? No. A discount is a reduction from the marked price; profit is the gain over the cost. They sit on different bases, and a single problem can involve both.
Why do two equal discounts not add to their sum? The second discount applies to the already-reduced price, so it removes less in absolute terms. Multiply the keep-fractions (0.90 × 0.90 = 0.81) to get the true combined effect.
In two-articles-same-price problems, why is it always a loss? The item sold at a loss had a higher cost than the one sold at a profit, so its bigger cost drags the total down. The net is always a loss of (x/10)² percent.
Tick every box and profit and loss becomes quick, confident points — and you'll never be fooled by a price tag in real life again.
Put it to the test with 1,928 practice questions on this topic.