Profit and Loss – Complete Concept Guide
Sainik School Entrance Examination | Full Notes + MCQs + Video Classes
1️⃣ Key Definitions
Cost Price (CP) → Price at which an article is purchased.
Selling Price (SP) → Price at which it is sold.
Profit (P) = SP − CP (when SP > CP)
Loss (L) = CP − SP (when SP < CP)
Marked Price (MP) → Printed price on the tag.
Discount (D) = MP − SP
💡 Shortcut Formulas:
SP = CP × (100 + Profit%) / 100
SP = CP × (100 − Loss%) / 100
CP = SP × 100 / (100 ± %)
SP = CP × (100 + Profit%) / 100
SP = CP × (100 − Loss%) / 100
CP = SP × 100 / (100 ± %)
Profit % = (Profit / CP) × 100
Loss % = (Loss / CP) × 100
2️⃣ Important Shortcuts
✔ Profit 20% → Multiply CP by 1.20
✔ Loss 20% → Multiply CP by 0.80
✔ Profit 25% → Multiply by 1.25
✔ Loss 10% → Multiply by 0.90
✔ 12.5% = 1/8
✔ 25% = 1/4
✔ 20% = 1/5
3️⃣ Example MCQs
Q1. CP = 500, SP = 650. Profit %?
Profit = 150 → (150/500) × 100 = 30%
✔ Correct Answer: 30%
Profit = 150 → (150/500) × 100 = 30%
✔ Correct Answer: 30%
Q2. CP = 800, Loss = 12.5%.
12.5% = 1/8 → Loss = 100 → SP = 720
12.5% = 1/8 → Loss = 100 → SP = 720
Q3. SP = 9000, Loss 10%.
CP = 9000 × 100 / 90 = 10,000
CP = 9000 × 100 / 90 = 10,000
Q4. CP = 200, Profit 20%.
SP = 200 × 1.20 = 240
SP = 200 × 1.20 = 240
Q5. MP = 1500, Discount 20%.
SP = 1500 × 0.80 = 1200
SP = 1500 × 0.80 = 1200
Q6. 15 pens cost 750, Profit 30%.
CP per pen = 50 → SP per pen = 65
CP per pen = 50 → SP per pen = 65
Q7. SP = 800, Loss 20%.
CP = 800 × 100 / 80 = 1000
CP = 800 × 100 / 80 = 1000
Q8. CP = 200, SP = 250.
Profit% = 25%
Profit% = 25%
Q9. SP = 12000, Profit 25%.
CP = 12000 × 100 / 125 = 10000
CP = 12000 × 100 / 125 = 10000
Q10. SP = 460, Loss 8%.
CP = 460 × 100 / 92 = 500
CP = 460 × 100 / 92 = 500
4️⃣ Why Important for Sainik School?
✔ Frequently asked topic
✔ Used in Mixture, Alligation
✔ Used in Simple Interest
✔ Used in Speed & Time
✔ Builds strong arithmetic foundation
