📊 Profit and Loss – SSC Cheat Sheet

🔢 Basic Formulas

Profit (P) = Selling Price (SP) – Cost Price (CP)
Loss (L) = Cost Price (CP) – Selling Price (SP)
Profit% = (Profit / CP) × 100
Loss% = (Loss / CP) × 100
SP = CP × (1 + Profit%)
SP = CP × (1 – Loss%)
CP = SP / (1 + Profit%)
CP = SP / (1 – Loss%)

🧠 Short Tricks

✅ If article is sold at x% profit and y% loss:

Overall % gain/loss = {(x – y) ± (xy / 100)}
➤ Use + if both profit or both loss
➤ Use – if one profit and one loss

✅ When two articles are sold at same price but one at x% profit and one at x% loss:

Overall Loss% = (x² / 100)

📝 Example:

Sold one at 20% profit and one at 20% loss.
Loss% = (20² / 100) = 4%

💡 Special Cases & Tricks

Case 1: If profit% and loss% are same on two items of equal selling price

Overall result is always loss

Case 2: If SP of two items is same and gain and loss is same %,

Overall loss = (common %)² / 100

🧠 Memorize This Table

Profit/Loss %	Multiplier
10% Profit	1.10
20% Profit	1.20
10% Loss	0.90
25% Loss	0.75

📘 SSC Previous Year Questions

🔹 Question 1 (SSC CGL 2022)

A shopkeeper gains 20% by selling an article for ₹360. What is the cost price?

Solution: SP = ₹360
Profit% = 20%
CP = SP / (1 + 20/100) = 360 / 1.20 = ₹300 ✅

🔹 Question 2 (SSC CHSL 2021)

A man sold two articles at ₹1000 each. On one, he made 20% profit and on the other, 20% loss. Find the overall gain or loss %.

Trick Used:
Same SP, same %, one profit one loss
Loss% = (20²)/100 = 400/100 = 4% Loss

🔹 Question 3 (SSC CGL Tier 1, 2019)

A vendor sells an article at a profit of 25%. If he had bought it at 20% less and sold it for ₹36 more, his profit would have been 40%. Find the cost price.

Let CP = ₹x
Then, SP = x × 1.25 = 1.25x
New CP = 0.8x, New SP = 1.25x + 36
New profit% = (1.25x + 36 – 0.8x) / 0.8x × 100 = 40

➡ Solve:
(0.45x + 36) / 0.8x × 100 = 40
➡ Final Answer: x = ₹200 ✅

🚀 Bonus Tips

Always express % as decimals when multiplying
If two SPs are equal but % change differs, apply (x² / 100) trick
For max accuracy, work with fractions rather than decimals in tough questions
Practice % to fraction:
- 25% → 1/4
- 20% → 1/5
- 12.5% → 1/8
- 50% → 1/2

🧠 Quick Practice Questions

Profit of 12.5% on CP. SP = ₹225. Find CP.
👉 CP = 225 / (1 + 0.125) = ₹200
Loss of 10%. CP = ₹500. Find SP.
👉 SP = 500 × (1 – 0.10) = ₹450
SP = ₹800, Profit = 25%. Find CP.
👉 CP = 800 / 1.25 = ₹640
CP = ₹1000, Loss = 15%. Find SP.
👉 SP = 1000 × 0.85 = ₹850

🧠 Rapid Revision Flash Card

💸 Profit = SP – CP 📉 Loss = CP – SP 📈 Profit% = (P/CP) × 100 📉 Loss% = (L/CP) × 100 💰 CP = SP / (1 + P%) or (1 – L%) 🪙 SP = CP × (1 + P%) or (1 – L%)

Profit and Loss Cheat Sheet for SSC Exams