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Chapter Outline & Learning Goals
By the end of this chapter, you will be able to:

Define Cost Price (CP), Selling Price (SP), Profit, Loss.

Calculate profit % and loss % correctly (always on CP).

Handle discount, marked price, and mixed scenarios.

Solve high‑yield exam traps like equal selling price with opposite % profit/loss.

Use ratio method (CP=100) to solve in seconds.

The ₹20 Sweet Trap (Your Hook)
A young boy bought a box of sweets for ₹200 and sold it to his friend for ₹220, thinking he made a ₹20 profit. The friend later sold the same box for ₹240. The boy said, “I made ₹20, he made ₹20 — so both earned equally.” Is that true? The boy’s cost was ₹200, profit ₹20 → 10% profit. The friend’s cost was ₹220, profit ₹20 → only about 9% profit. Same profit in rupees, but completely different in percentage. This tiny shift in viewpoint causes most of the confusion in Profit & Loss. Let’s clear it forever.

I Know You Find It Tricky — And That’s Okay
If you ever thought “Profit % is on SP” or “Discount is on CP,” you are not alone. Almost every learner makes these mistakes at first. Our goal is to turn this into an unbreakable mental habit, with weird memory tricks and bite‑sized logic. Ready? Let’s walk step by step.

1. The Two Pillars: CP and SP

Cost Price (CP): The price you pay to acquire or make something.

Selling Price (SP): The price at which you finally sell it.

Profit = SP − CP (when SP > CP)
Loss = CP − SP (when CP > SP)

🧠 Active Recall: You buy a pen for ₹15 and sell it for ₹20. Profit in rupees? (Answer: ₹5) And what if you sold it for ₹12? (Loss of ₹3)

2. The Percentage Rule That Everyone Gets Wrong
   The percentage of profit or loss is always calculated on the Cost Price — never on the Selling Price.

Profit % = (Profit ÷ CP) × 100

Loss % = (Loss ÷ CP) × 100

Example: CP = ₹200, sold for ₹250. Profit = ₹50, Profit % = (50/200)×100 = 25%. Why 25%? Because the ₹50 extra is a quarter of the original cost.

🧠 Active Recall: If CP = ₹500 and SP = ₹400, what is the loss %? (Loss = ₹100, so (100/500)×100 = 20% loss.)

Weird Memory Trick (Mnemonic):
Think of CP as “Child’s Piggy bank” and SP as “Show‑off Price.” A child knows exactly how much money was in the piggy bank (CP). Whatever extra she gets is a percentage of that starting money, not of the flashy price tag. So chant: “Percent always on the Piggy bank, not the Show‑off!” — weird but sticky.

3. The Super Shortcut: Assume CP = 100
   When you see a percentage like “10% profit” or “25% loss,” immediately imagine CP = ₹100. Then:

At 10% profit, SP = ₹110.

At 25% loss, SP = ₹75.

This unlocks ratios: CP : SP = 100 : (100±P). You can now solve most problems without ever touching fractions.

🧠 Active Recall: A shopkeeper sells an item at 20% profit. If SP is ₹480, find CP. (Assume CP=100, SP=120. So 120 → ₹480, thus 100 → CP = (480/120)×100 = ₹400.)

4. Marked Price & Discount — The Dressing Room Drama
   Marked Price (MP) is the price tag a seller puts on an item — often inflated. Discount is always given on MP.

SP = MP − Discount (or SP = MP × (100 − Discount%)/100)

Profit/Loss is still calculated on CP.

Mnemonic: “Discount De‑tags the MP, but Profit measures on CP.” Imagine the price tag (MP) is a balloon; discount pricks it to SP, but your cost (CP) never changes its core.

🧠 Active Recall: CP = ₹600, MP = ₹800, Discount = 10%. Find Profit %.
SP = 800 × 90% = ₹720. Profit = 720−600 = ₹120. Profit % = (120/600)×100 = 20%.

5. The Deadly Trap: Same Selling Price, Equal % Profit & Loss
   If you sell two items at the same price, one at x% profit and the other at x% loss, you ALWAYS suffer an overall loss. The loss % = (x²/100)%.
   Example: x = 20%, loss = (20²/100)% = 4% loss. Try it — you’ll never get a no‑profit‑no‑loss.

Why? Because the loss is on a higher CP (the item sold at loss has a larger CP than the one sold at profit). The math hides a little monster.

🧠 Active Recall: Two watches sold for ₹990 each, one at 10% profit, the other at 10% loss. Overall result? (Loss % = (10²/100)% = 1% loss)

6. When Profit Equals Loss in Rupees (Two Different SPs)
   Sometimes the question says: “Selling at ₹800 gives as much profit as selling at ₹600 gives loss.” Then CP is simply the average of the two SPs: CP = (800+600)/2 = ₹700. A gift from algebra.

🧠 Active Recall: Selling a book for ₹450 gives as much loss as selling for ₹510 gives profit. CP? ( (450+510)/2 = ₹480 )

Summary Table – Keep This on Your Wall

🧠 Review after 2 days:
Write down the above table from memory. Create five small numerical problems using every row. Solve them without looking. This will move the concepts from your short‑term memory into your long‑term exam armoury. You’ve got this!