UGC NET Paper 1 Unit 5 Topic 3: Mathematical Aptitude - Profit, Loss & Interest

💰 UGC NET Paper 1 Unit 5 Profit, Loss & Interest

📊 Master profit/loss calculations, discount formulas, and simple/compound interest problems with this comprehensive guide. Crucial for 4-6 NET questions per exam.

💡 Quick Summary: Key concepts in commercial mathematics:

1. Profit/Loss: CP, SP, Marked Price, Discount
2. Simple Interest: Fixed percentage on principal
3. Compound Interest: Interest on interest

1. Profit and Loss

🔹 Basic Formulas

Profit = Selling Price (SP) - Cost Price (CP)
Loss = CP - SP
Profit % = (Profit/CP) × 100
Loss % = (Loss/CP) × 100

🔹 Marked Price & Discount

Concept	Formula	Example
Discount	MP - SP	MP = ₹500, Discount = 20% → SP = ₹400
Successive Discount	Equivalent discount = d₁ + d₂ - (d₁×d₂)/100	10% + 20% = 28% equivalent discount
False Weight	Profit% = (Error)/(True weight - Error) × 100	Uses 900g instead of 1kg → 11.11% profit

📌 Memory Aid: "PLMD" for Profit/Loss concepts - Profit, Loss, Marked Price, Discount

2. Simple Interest

Key Features:

• Calculated only on principal amount
• Same interest amount every year
• Formula: SI = (P × R × T)/100

🔹 Important Concepts

Concept	Formula	Example
Basic SI	SI = (P×R×T)/100	P=1000, R=5%, T=2y → SI=100
Amount	A = P + SI	Above example → A=1100
Rate Calculation	R = (SI×100)/(P×T)	SI=200, P=1000, T=2 → R=10%

🔹 Time Conversion

1. Months to Years: Divide by 12 (6 months = 0.5 years)
2. Days to Years: Divide by 365 (73 days = 0.2 years)
3. Exact Days: Use (Number of days/365) in formula

3. Compound Interest

Characteristics:

• Interest on principal + accumulated interest
• Yields more than simple interest
• Formula: A = P(1 + r/n)^nt

🔹 Key Formulas

Annual compounding: A = P(1 + r/100)^t
Half-yearly: A = P(1 + (r/2)/100)^2t
Quarterly: A = P(1 + (r/4)/100)^4t

🔹 Comparison with Simple Interest

Parameter	Simple Interest	Compound Interest
Interest Calculation	Only on principal	Principal + Accumulated interest
Growth	Linear	Exponential
Amount Formula	P + (P×R×T)/100	P(1 + R/100)T

4. Problem Solving Strategies

Problem Type	Approach	Example
Profit/Loss %	Always calculate % on CP	CP=100, SP=120 → Profit=20%
Successive Discount	Use multiplicative formula	10%+20% = 0.9×0.8=0.72 → 28% off
CI vs SI Difference	For 2 years: Difference = P(r/100)2	P=1000, r=10% → Diff=10

🔥 Most Repeated NET Questions:

1. A shopkeeper sells at 20% profit. If CP=₹250, SP=? (Answer: ₹300)
2. Difference between CI and SI for 2 years at 10% on ₹1000? (Answer: ₹10)
3. Equivalent discount for 10%+20%? (Answer: 28%)
4. If SI for 3 years is ₹300 at 5% rate, principal=? (Answer: ₹2000)
5. CI on ₹5000 at 8% compounded quarterly for 1 year? (Answer: ₹412.16)

📝 Common Mistakes to Avoid

🔹 Pitfalls in Calculations

Mistake	Explanation	Correct Approach
Profit % on SP	Calculating % on selling price instead of CP	Always base % calculations on CP
Simple addition of discounts	Adding 10%+20%=30% instead of 28%	Use multiplicative formula
CI frequency confusion	Not adjusting rate and time for compounding periods	For quarterly: r→r/4, t→4t

🚀 Advanced Applications

• Population Growth: Similar to CI calculations
  Population increases 5% annually. Current=20000 → After 2 years?
  Solution: 20000×(1.05)² = 22050
• Depreciation: Similar to CI but decreasing
  Machine value depreciates 10% yearly. Original=₹50000 → After 3 years?
  Solution: 50000×(0.9)³ = ₹36450
• Installment Payments: EMI calculations using CI concepts

📌 Exam Tip: For quick calculations:

1. 10% of ₹500 → ₹50 (move decimal one place left)
2. 5% = 10%/2 → ₹25 in above case
3. 20% = 10%×2 → ₹100
4. 15% = 10% + 5% → ₹75

💡 Pro Strategy: Practice percentage equivalents (1/8=12.5%, 1/6≈16.66% etc.). Master mental math shortcuts for faster calculations in exam!