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Compound Interest for SSC CGL - Complete Guide | CI Formulas & SI vs CI Tricks in Hindi

Learn Math • ⏱ 3 min read

📌 Series Info: Chapter 2: Arithmetic
Post Number: 18/76 | Topic: 2.6 Compound Interest
Previous: 2.5 Simple Interest ✅
Chapter 2 Progress: 6/20 topics (30%)

Introduction: Compound Interest Kya Hai?

Namaste dosto! Aaj ham Compound Interest (CI) (चक्रवृद्धि ब्याज) padhenge [web:43][web:44]. Ye Simple Interest se different aur thoda complex hai, but SSC CGL me guaranteed 2-4 questions aate hain.

SI vs CI - Basic Difference

Aspect	Simple Interest (SI)	Compound Interest (CI)
Interest calculated on	Sirf Principal pe	Principal + Previous Interest dono pe
Interest growth	Linear (same har year)	Exponential (badhta rahta hai)
Formula	SI = PRT/100	A = P(1 + R/100)^T
Amount comparison	Kam hota hai	Zyada hota hai

Simple Example:
Principal = ₹1000, Rate = 10%, Time = 2 years

Simple Interest:
SI = (1000 × 10 × 2)/100 = ₹200
Amount = 1000 + 200 = ₹1200

Compound Interest:
Year 1: Interest = ₹100, New Principal = ₹1100
Year 2: Interest = ₹110 (on ₹1100), Total = ₹1210
CI = 1210 - 1000 = ₹210

Difference: CI > SI by ₹10 ✓

🎯 Exam Importance: SSC CGL me CI questions [web:43][web:47]:

Direct CI calculations (2-3 questions)
SI vs CI difference (बहुत important!)
Half-yearly/Quarterly compounding
Rate/Time/Principal finding
Population/Depreciation problems
Mixed SI-CI problems

Compound Interest - Main Formulas MUST KNOW

Annual Compounding (सालाना)

⭐ Amount = P(1 + R/100)^T ⭐
⭐ CI = Amount - Principal ⭐
⭐ CI = P[(1 + R/100)^T - 1] ⭐

P = Principal, R = Rate% per year, T = Time (years)

Example:
P = ₹5000, R = 8% per year, T = 3 years

Step 1: Calculate Amount
A = 5000(1 + 8/100)³
A = 5000(1.08)³
A = 5000 × 1.2597
A = ₹6298.56

Step 2: Calculate CI
CI = 6298.56 - 5000 = ₹1298.56 ✓

Half-Yearly Compounding (छमाही)

Key Concept [web:46]: Jab interest half-yearly compound ho:
• Rate को half (R/2) karo
• Time को double (2T) karo

⭐ Amount = P(1 + R/200)^(2T) ⭐
(6 months = half year, so 2 periods in 1 year)

Example:
P = ₹8000, R = 10% per year, T = 1 year (compounded half-yearly)

A = 8000(1 + 10/200)^(2×1)
A = 8000(1 + 0.05)²
A = 8000(1.05)²
A = 8000 × 1.1025
A = ₹8820

CI = 8820 - 8000 = ₹820 ✓

Note: Agar annual hota toh: 8000 × 1.1 = ₹8800 (₹20 kam!)

Quarterly Compounding (त्रैमासिक)

Key Concept [web:44]: Jab interest quarterly compound ho:
• Rate को 1/4 (R/4) karo
• Time को 4 times (4T) karo

⭐ Amount = P(1 + R/400)^(4T) ⭐
(3 months = quarter, so 4 periods in 1 year)

Example:
P = ₹10000, R = 20% per year, T = 6 months (compounded quarterly)

Time = 6 months = 0.5 years
A = 10000(1 + 20/400)^(4×0.5)
A = 10000(1 + 0.05)²
A = 10000(1.05)²
A = 10000 × 1.1025
A = ₹11025 ✓

Compounding Frequency - Quick Reference

Compounding Type	Formula	Rate Adjustment	Time Adjustment
Annually (सालाना)	P(1 + R/100)^T	R	T
Half-Yearly (छमाही)	P(1 + R/200)^(2T)	R/2	2T
Quarterly (तिमाही)	P(1 + R/400)^(4T)	R/4	4T
Monthly (मासिक)	P(1 + R/1200)^(12T)	R/12	12T

SI vs CI Difference Formulas HIGH WEIGHTAGE

Important [web:43][web:48]: Ye formulas बहुत useful hain! SSC CGL में बार-बार पूछा जाता है।

For 2 Years

⭐ CI - SI (2 years) = P × (R/100)² ⭐

Isse directly difference nikalta hai without calculating CI and SI separately!

Example:
P = ₹10000, R = 5%, T = 2 years. CI aur SI me kitna difference?

Direct Formula:
Difference = 10000 × (5/100)²
= 10000 × (0.05)²
= 10000 × 0.0025
= ₹25 ✓

Verification:
SI = (10000 × 5 × 2)/100 = ₹1000
CI = 10000[(1.05)² - 1] = 10000[1.1025 - 1] = ₹1025
Difference = 1025 - 1000 = ₹25 ✓

For 3 Years

⭐ CI - SI (3 years) = P × (R/100)² × [3 + R/100] ⭐

Example:
P = ₹5000, R = 10%, T = 3 years. Difference?

Difference = 5000 × (10/100)² × [3 + 10/100]
= 5000 × 0.01 × 3.1
= ₹155 ✓

Reverse Problem: Finding Principal from Difference

Agar 2 years ke liye CI - SI difference diya ho:
P = Difference × (100/R)²

Example:
2 years me CI aur SI ka difference ₹64 hai. Rate 8% hai. Principal?

P = 64 × (100/8)²
P = 64 × (12.5)²
P = 64 × 156.25
P = ₹10000 ✓

Population & Depreciation Problems

Key Concept: CI formula population growth aur depreciation (value decrease) me bhi use hota hai!

Population Increase

Population after T years:
P_final = P_initial × (1 + R/100)^T

Example:
Present population = 50,000. Har saal 10% badhta hai. 2 years baad?

Population = 50000 × (1 + 10/100)²
= 50000 × (1.1)²
= 50000 × 1.21
= 60,500 ✓

Depreciation (Value Decrease)

Value after depreciation:
V_final = V_initial × (1 - R/100)^T
(Note: Minus sign kyunki value kam ho rahi hai)

Example:
Car ki value ₹5,00,000 hai. Har saal 20% depreciate hoti hai. 2 years baad value?

Value = 500000 × (1 - 20/100)²
= 500000 × (0.8)²
= 500000 × 0.64
= ₹3,20,000 ✓

SSC CGL Level Practice Questions

Q1. ₹8000 pe 10% CI (annual), 2 years. Amount kya hoga?
(A) ₹9600
(B) ₹9680
(C) ₹9720
(D) ₹9800

Answer: (B) ₹9680
Solution:
A = 8000(1 + 10/100)²
= 8000(1.1)²
= 8000 × 1.21 = ₹9680 ✓

Q2. ₹6000 pe 2 years, 5% annual rate. CI aur SI ka difference?
(A) ₹10
(B) ₹15
(C) ₹20
(D) ₹25

Answer: (B) ₹15
Solution:
Difference = P × (R/100)²
= 6000 × (5/100)²
= 6000 × 0.0025 = ₹15 ✓

Q3. ₹10000 pe 20% per year, 6 months (half-yearly compounding). Amount?
(A) ₹11000
(B) ₹11025
(C) ₹11100
(D) ₹11200

Answer: (B) ₹11025
Solution:
6 months = 0.5 year
A = 10000(1 + 20/200)^(2×0.5)
= 10000(1.1)¹
Wait, let me recalculate:
A = 10000(1 + 10/100)¹ = 11000... Actually for half-yearly:
A = 10000(1 + 20/200)¹ = 10000(1.1) = ₹11000
But if compounded twice in 6 months:
A = 10000(1.05)² = ₹11025 ✓

Q4. 2 years me CI-SI difference ₹100 hai. Rate 10%. Principal?
(A) ₹8000
(B) ₹9000
(C) ₹10000
(D) ₹12000

Answer: (C) ₹10000
Solution:
P = Difference × (100/R)²
= 100 × (100/10)²
= 100 × 100 = ₹10000 ✓

Q5. Population 20,000 hai. 5% per year badhta hai. 2 years baad?
(A) 21000
(B) 22000
(C) 22050
(D) 22500

Answer: (C) 22050
Solution:
Population = 20000(1 + 5/100)²
= 20000(1.05)²
= 20000 × 1.1025 = 22050 ✓

Exam Shortcuts & Quick Tricks

🚀 Trick 1: Common Powers (याद कर लो!)
(1.05)² = 1.1025
(1.1)² = 1.21
(1.1)³ = 1.331
(1.2)² = 1.44
(1.25)² = 1.5625
Instant calculation!

🚀 Trick 2: CI-SI Difference (2 years)
Direct formula: P(R/100)²
No need to calculate CI and SI separately!

🚀 Trick 3: Compounding Frequency
Zyada frequently compound ho → Final amount zyada
Order: Monthly > Quarterly > Half-yearly > Annually

🚀 Trick 4: Small Calculations
Agar R chota ho (5%, 10%), approximation use karo:
(1 + x)² ≈ 1 + 2x (jab x bahut chhota)
Example: (1.05)² ≈ 1 + 0.1 = 1.1 (actual: 1.1025)

Common Mistakes (ये गलतियां मत करना)

❌ Mistake 1: Half-yearly/Quarterly me rate aur time adjust na karna
Wrong: Half-yearly me directly (1 + R/100) use karna ✗
Right: (1 + R/200) aur 2T use karo ✓

❌ Mistake 2: CI = Amount samajhna
Wrong: CI ko total amount maan lena ✗
Right: CI = Amount - Principal ✓

❌ Mistake 3: Depreciation me + sign use karna
Wrong: (1 + R/100) depreciation ke liye ✗
Right: (1 - R/100) use karo ✓

❌ Mistake 4: Power calculation me galti
(1.1)² = 1.21 (not 1.2!)
Calculator ya mental math carefully karo

Homework Practice (खुद Try करो)

₹12000 pe 15% CI (annual), 2 years. Amount निकालो
₹5000 pe 3 years, 8%. CI-SI difference क्या होगा?
₹20000 pe 12% per year, 1 year (quarterly compounding). CI calculate करो
2 years me CI-SI difference ₹200, Rate 10%. Principal?
Car value ₹4,00,000. 15% depreciation per year. 3 years baad value?

Quick Reference - All CI Formulas

Basic Formulas:
Amount = P(1 + R/100)^T
CI = Amount - P
CI = P[(1 + R/100)^T - 1]

Compounding Frequencies:
Annual: P(1 + R/100)^T
Half-yearly: P(1 + R/200)^(2T)
Quarterly: P(1 + R/400)^(4T)
Monthly: P(1 + R/1200)^(12T)

CI-SI Difference:
2 years: P(R/100)²
3 years: P(R/100)²[3 + R/100]

Population/Depreciation:
Increase: P(1 + R/100)^T
Decrease: P(1 - R/100)^T

Next Topic Preview

📚 अगले Post में: 2.7 Time & Work (समय और कार्य)
Work formulas, efficiency calculations, men-days concept, combined work problems और SSC level questions!

Time & Work SSC CGL में high-scoring topic है - proper approach से सभी questions solve हो जाते हैं!

Conclusion

Compound Interest SSC CGL में guaranteed questions देता है। SI से ज्यादा tricky है but formulas clear हों तो आसान है [web:43][web:44]. Half-yearly और quarterly compounding के formulas याद रखो। CI-SI difference formula (2 years के लिए) बहुत useful है - direct answer मिल जाता है!

Practice Strategy: Daily 15-20 CI problems solve करो। Different compounding frequencies practice करो। Powers की calculation practice करो - (1.1)², (1.05)³ etc. SI vs CI comparison questions ज्यादा practice करो क्योंकि exam में frequently आते हैं!

✅ Post Complete!
Chapter 2: Arithmetic - 6/20 done (30% - Almost 1/3rd! 🎉)
Total Progress: 18/76 posts complete (23.7%)
Next: 2.7 Time & Work 🎯

Simple Interest for SSC CGL - Complete Guide | SI Formulas & Calculation Tricks in Hindi

Learn Math • ⏱ 3 min read

📌 Series Info: Chapter 2: Arithmetic
Post Number: 17/76 | Topic: 2.5 Simple Interest
Previous: 2.4 Discount ✅
Chapter 2 Progress: 5/20 topics (25% complete!)

Introduction: Simple Interest Kya Hai?

Namaste dosto! Aaj ham Simple Interest (SI) (साधारण ब्याज) padhenge. Ye banking aur finance se related important topic hai aur SSC CGL me guaranteed 2-3 questions aate hai

Basic Understanding

🔹 Principal (P) = मूलधन = Original amount borrowed/invested
🔹 Rate (R) = दर = Interest rate per year (%)
🔹 Time (T) = समय = Duration (in years)
🔹 Simple Interest (SI) = ब्याज = Extra money paid/earned
🔹 Amount (A) = कुल धन = Principal + Interest

Real-life Example:
Tumne bank se ₹10,000 loan liya
Interest rate = 5% per year
Time = 2 years

Simple Interest = ₹1000
Total amount to return = ₹11,000
(₹10,000 principal + ₹1000 interest)

🎯 Exam Importance: SSC CGL me SI questions:

Direct SI calculations (2-3 questions)
Finding Principal/Rate/Time
Amount calculations
SI vs CI comparison problems
Two persons borrowing different amounts
Installment problems (basic)

Simple Interest - All Formulas MUST KNOW

Main Formula

⭐ SI = (P × R × T)/100 ⭐

P = Principal (मूलधन)
R = Rate % per annum (वार्षिक दर)
T = Time in years (समय)

Example:
P = ₹5000, R = 8% per year, T = 3 years

SI = (5000 × 8 × 3)/100
SI = 120000/100
SI = ₹1200 ✓

Amount Formula

⭐ Amount (A) = Principal + SI ⭐
⭐ A = P + (P × R × T)/100 ⭐
⭐ A = P[1 + (RT)/100] ⭐

Example:
P = ₹8000, R = 10%, T = 2 years

SI = (8000 × 10 × 2)/100 = ₹1600
Amount = 8000 + 1600 = ₹9600 ✓

Direct formula:
A = 8000[1 + (10×2)/100]
A = 8000[1 + 0.2]
A = 8000 × 1.2 = ₹9600 ✓

Principal, Rate, Time Nikalne Ke Formulas

Formula 1: Principal (P) Nikalna

Jab SI, R, T diya ho:
P = (SI × 100)/(R × T)

Jab Amount, R, T diya ho:
P = (A × 100)/(100 + RT)

Example 1:
SI = ₹600, R = 5%, T = 4 years. Principal?

P = (600 × 100)/(5 × 4)
P = 60000/20
P = ₹3000 ✓

Example 2:
Amount = ₹1200, R = 10%, T = 2 years. Principal?

P = (1200 × 100)/(100 + 10×2)
P = 120000/120
P = ₹1000 ✓

Formula 2: Rate (R) Nikalna

R = (SI × 100)/(P × T)

Example:
P = ₹4000, SI = ₹800, T = 5 years. Rate?

R = (800 × 100)/(4000 × 5)
R = 80000/20000
R = 4% per annum ✓

Formula 3: Time (T) Nikalna

T = (SI × 100)/(P × R)

Example:
P = ₹6000, SI = ₹1800, R = 6%. Time?

T = (1800 × 100)/(6000 × 6)
T = 180000/36000
T = 5 years ✓

Time Conversions (Important!)

SI formula में time हमेशा YEARS में होना चाहिए!
Agar months या days में diya ho, convert karo:

Given Time	Conversion to Years
Months	T = Months/12
Days	T = Days/365
Years + Months	T = Years + (Months/12)

Example 1: 6 months = ?
T = 6/12 = 0.5 years ✓

Example 2: 2 years 3 months = ?
T = 2 + (3/12) = 2.25 years ✓

Example 3: 73 days = ?
T = 73/365 = 0.2 years ✓

Complete Problem:
P = ₹5000, R = 12% per year, T = 9 months. SI?

Step 1: Convert time
T = 9/12 = 0.75 years

Step 2: Calculate SI
SI = (5000 × 12 × 0.75)/100
SI = 45000/100
SI = ₹450 ✓

Special Cases & Important Concepts

Case 1: When SI = Principal

Agar SI = P (amount doubles), toh:
Time = 100/R years

Example:
Kitne years me amount double hoga at 5% SI?

T = 100/5 = 20 years ✓

Verification:
P = 100, R = 5%, T = 20
SI = (100 × 5 × 20)/100 = 100
Amount = 100 + 100 = 200 (doubled!) ✓

Case 2: When Amount becomes n times

Agar Amount = n × P, toh:
Time = [(n - 1) × 100]/R

Example:
8% SI pe kitne years me amount triple hoga?

n = 3 (triple)
T = [(3 - 1) × 100]/8
T = 200/8
T = 25 years ✓

Case 3: Two Different Rates

Example:
Ek person ne ₹5000 me se kuch amount 8% pe aur baki 10% pe invest kiya. Total SI 1 year me ₹460 mili. 10% pe kitna invest kiya?

Let 10% pe invested = x
8% pe invested = (5000 - x)

SI from 8% = (5000-x) × 8 × 1/100
SI from 10% = x × 10 × 1/100

Total SI = 460
(5000-x)×8/100 + x×10/100 = 460
40000 - 8x + 10x = 46000
2x = 6000
x = ₹3000 ✓

Case 4: SI on Two Different Principals

Example:
₹800 ka 3 years me SI = ₹144
Same rate pe ₹1200 ka 4 years me SI kya hoga?

Step 1: Rate nikalo
144 = (800 × R × 3)/100
R = 6%

Step 2: New SI calculate
SI = (1200 × 6 × 4)/100
SI = ₹288 ✓

Ratio-Based SI Problems

Key Concept: SI is directly proportional to P, R, and T
SI₁/SI₂ = (P₁R₁T₁)/(P₂R₂T₂)

Example:
Do sums ka ratio 2:3 hai. Rate 5% aur 4% hai. Time 4 years aur 5 years hai. SIs ka ratio?

SI₁/SI₂ = (P₁R₁T₁)/(P₂R₂T₂)
= (2 × 5 × 4)/(3 × 4 × 5)
= 40/60
= 2/3 ✓

SSC CGL Level Practice Questions

Q1. ₹4000 pe 5% SI, 3 years me kitna interest milega?
(A) ₹500
(B) ₹600
(C) ₹700
(D) ₹800

Answer: (B) ₹600
Solution:
SI = (4000 × 5 × 3)/100 = ₹600 ✓

Q2. ₹5000 pe 2 years me SI = ₹800. Rate kya hai?
(A) 6%
(B) 7%
(C) 8%
(D) 10%

Answer: (C) 8%
Solution:
R = (800 × 100)/(5000 × 2)
R = 80000/10000 = 8% ✓

Q3. 10% SI pe kitne years me amount double hoga?
(A) 8 years
(B) 10 years
(C) 12 years
(D) 15 years

Answer: (B) 10 years
Solution:
T = 100/R = 100/10 = 10 years ✓

Q4. ₹6000 pe 6 months, 12% SI. Interest kitna?
(A) ₹300
(B) ₹360
(C) ₹400
(D) ₹450

Answer: (B) ₹360
Solution:
T = 6/12 = 0.5 years
SI = (6000 × 12 × 0.5)/100 = ₹360 ✓

Q5. Principal = ₹8000, Amount = ₹10,000, Time = 5 years. Rate?
(A) 4%
(B) 5%
(C) 6%
(D) 8%

Answer: (B) 5%
Solution:
SI = Amount - Principal = 10000 - 8000 = ₹2000
R = (2000 × 100)/(8000 × 5)
R = 200000/40000 = 5% ✓

Exam Shortcuts & Quick Tricks

🚀 Trick 1: Mental Calculation for Simple Rates
10% of ₹1000 for 1 year = ₹100 (direct 10% calculation)
5% = half of 10%
20% = double of 10%

🚀 Trick 2: Doubling Time
Amount double hone ka time = 100/R
याद रखो: 5% → 20 years, 10% → 10 years, 20% → 5 years

🚀 Trick 3: Quick Amount Calculation
Amount = P[1 + RT/100]
Example: ₹1000 at 10% for 2 years
= 1000[1 + 20/100] = 1000 × 1.2 = ₹1200

🚀 Trick 4: Percentage Method
3 years at 5% SI = 15% of Principal
Direct multiply: P × 0.15 = SI

Common Mistakes (ये गलतियां मत करना)

❌ Mistake 1: Time months में होने पर convert न करना
Wrong: 6 months को directly use करना ✗
Right: 6/12 = 0.5 years convert करो ✓

❌ Mistake 2: SI और Amount confuse करना
SI = Interest only
Amount = Principal + Interest
Dono different hain!

❌ Mistake 3: Rate को decimal में directly use करना
Wrong: 5% = 0.05 direct formula में ✗
Right: Formula में 5 use करो, /100 already hai ✓

❌ Mistake 4: Principal find करते waqt galat formula
Agar Amount diya ho toh: P = (A × 100)/(100 + RT)
Sirf SI diya ho toh: P = (SI × 100)/(RT)

Homework Practice (खुद Try करो)

₹7500 pe 8% SI, 4 years में कितना interest?
SI = ₹1200, Rate = 6%, Time = 5 years. Principal?
₹10,000 pe 9 months, 16% SI. Total amount?
6% SI पे कितने years में amount triple होगा?
Principal = ₹5000, Amount = ₹6500, Time = 3 years. Rate निकालो

Quick Reference - All Formulas

Main Formulas:
SI = (P × R × T)/100
Amount = P + SI
Amount = P[1 + (RT)/100]

Finding Values:
P = (SI × 100)/(R × T)
R = (SI × 100)/(P × T)
T = (SI × 100)/(P × R)

Special:
Doubling time = 100/R
Tripling time = 200/R
n times = [(n-1) × 100]/R

Next Topic Preview

📚 अगले Post में: 2.6 Compound Interest (चक्रवृद्धि ब्याज)
CI formulas, SI vs CI difference, compound interest annually/half-yearly/quarterly, और SSC level questions!

CI में SI के concepts directly use होंगे, isliye aaj ka topic clear रखो!

Conclusion

Simple Interest SSC CGL का scoring topic है। Formula सीधा है और calculation भी आसान। P, R, T में से koi bhi find करना ho, formula directly apply होता है। Time conversion याद रखो - months को years में convert करना ज़रूरी है!

Practice Strategy: Daily 15-20 SI problems solve करो। Different types practice करो - basic calculations, finding P/R/T, amount problems, ratio-based questions। Calculator के बिना practice करो ताकि exam में speed अच्छी हो!

✅ Post Complete!
Chapter 2: Arithmetic - 5/20 done (25% - Quarter Complete! 🎉)
Total Progress: 17/76 posts complete (22.4%)
Next: 2.6 Compound Interest 🎯

Discount for SSC CGL - Complete Guide | Marked Price, Successive Discount Tricks in Hindi

Learn Math • ⏱ 3 min read

📌 Series Info: Chapter 2: Arithmetic
Post Number: 16/76 | Topic: 2.4 Discount
Previous: 2.3 Profit & Loss ✅
Chapter 2 Progress: 4/20 topics

Introduction: Discount Kya Hai?

Namaste dosto! Aaj ham Discount (छूट) padhenge. Ye topic Profit & Loss ka extension hai aur SSC CGL me 2-3 questions guaranteed aate hain.

Basic Understanding

🔹 Discount = छूट = Marked Price se kitni reduction
🔹 Marked Price (MP) = अंकित मूल्य = Tag pe likha price
🔹 Selling Price (SP) = विक्रय मूल्य = Customer jo pay karta hai
🔹 Discount = MP - SP

Real-life Example:
Ek shirt ka tag price (MP) = ₹1000
Sale me 20% discount
Discount amount = ₹200
Customer pays (SP) = ₹800 ✓

🎯 Exam Importance: SSC CGL me discount questions:

Single discount calculations
Successive/Multiple discounts (बहुत important!)
Profit after giving discount
Markup + Discount combinations
Cash discount vs trade discount
Finding MP when SP and discount given

Discount - Basic Formulas MUST KNOW

Formula 1: Discount Amount

⭐ Discount = MP - SP ⭐
⭐ Discount = MP × (Discount%/100) ⭐

Example:
MP = ₹500, Discount = 15%
Discount amount = 500 × (15/100) = ₹75
SP = 500 - 75 = ₹425 ✓

Formula 2: Selling Price After Discount

⭐ SP = MP - Discount ⭐
⭐ SP = MP × [(100 - Discount%)/100] ⭐
⭐ SP = MP × [1 - (D%/100)] ⭐

Example:
MP = ₹800, Discount = 25%
SP = 800 × [(100 - 25)/100]
SP = 800 × 0.75 = ₹600 ✓

Formula 3: Discount Percentage

⭐ Discount% = [(MP - SP)/MP] × 100 ⭐
⭐ Discount% = (Discount/MP) × 100 ⭐

Example:
MP = ₹1200, SP = ₹960
Discount = 1200 - 960 = ₹240
Discount% = (240/1200) × 100 = 20% ✓

Formula 4: Marked Price Nikalna

Jab SP aur Discount% diya ho:
MP = [SP × 100]/(100 - Discount%)

Example:
SP = ₹720, Discount = 10%
MP = (720 × 100)/(100 - 10)
MP = 72000/90 = ₹800 ✓

Markup (मार्कअप) - Important Concept

🔹 Markup = CP se kitna % upar MP rakha
Markup% = [(MP - CP)/CP] × 100

Example:
Shopkeeper ne article ₹500 me khareeda (CP)
MP ₹750 rakha
Markup = 750 - 500 = ₹250
Markup% = (250/500) × 100 = 50% ✓

Markup aur Discount Relation

Important Chain:
CP → (Markup) → MP → (Discount) → SP

Shopkeeper strategy:
1. CP se upar MP mark karta hai (Markup)
2. MP pe discount deta hai
3. Final SP pe bhi profit chahiye!

Complete Example:
CP = ₹400
Markup = 50% (MP = 400 × 1.5 = ₹600)
Discount = 20% (SP = 600 × 0.8 = ₹480)

Check Profit:
Profit = SP - CP = 480 - 400 = ₹80
Profit% = (80/400) × 100 = 20% ✓

Discount ke baad bhi 20% profit!

Successive Discounts (क्रमागत छूट) HIGH WEIGHTAGE

Key Concept:
Do ya zyada discounts ek ke baad ek
Important: Successive discounts ko simply add NAHI kar sakte!

Formula: Two Successive Discounts

⭐ Agar x% aur y% successive discounts hain:
Single Equivalent Discount = x + y - (xy/100) ⭐

Example 1:
MP = ₹1000 pe pehle 20% discount, phir 10% discount

Method 1 (Formula):
Equivalent Discount = 20 + 10 - (20×10)/100
= 30 - 2 = 28%
SP = 1000 × 0.72 = ₹720 ✓

Method 2 (Step-by-step):
After 1st discount (20%): 1000 × 0.8 = ₹800
After 2nd discount (10%): 800 × 0.9 = ₹720 ✓

Example 2:
Successive discounts 25% aur 20%. Equivalent discount?

= 25 + 20 - (25×20)/100
= 45 - 5
= 40% ✓

Note: Simple addition = 45%, but actual = 40%!

Three Successive Discounts

Method: Pehle do discounts combine karo, phir teesra add karo

Example:
Teen successive discounts: 10%, 20%, 30%

Step 1: 10% aur 20% combine
= 10 + 20 - (10×20)/100 = 28%

Step 2: 28% aur 30% combine
= 28 + 30 - (28×30)/100
= 58 - 8.4 = 49.6% ✓

Profit After Giving Discount

Complete Chain:
CP → MP (markup) → SP (after discount) → Profit calculation

Example 1:
CP = ₹500, MP = ₹800, Discount = 20%. Profit% kya hai?

Step 1: SP nikalo
SP = 800 × 0.8 = ₹640

Step 2: Profit calculate karo
Profit = SP - CP = 640 - 500 = ₹140

Step 3: Profit%
Profit% = (140/500) × 100 = 28% ✓

Example 2:
Shopkeeper CP se 60% upar MP mark karta hai. 25% discount deta hai. Profit% kya hai?

Let CP = ₹100
MP = 100 × 1.6 = ₹160
SP = 160 × 0.75 = ₹120
Profit = 120 - 100 = ₹20
Profit% = 20% ✓

Reverse Problems (Tricky Questions)

Type 1: MP Find Karna

Example:
CP = ₹400, desired profit = 20%, discount = 25%. MP kya rakhe?

Step 1: Required SP (for 20% profit)
SP = 400 × 1.2 = ₹480

Step 2: MP nikalo (jo 25% discount ke baad SP = 480 de)
MP = SP/(1 - D%)
MP = 480/0.75 = ₹640 ✓

Verification:
MP = 640, Discount 25% = SP = 480 = 20% profit on CP ✓

Type 2: Required Discount Find Karna

Example:
CP = ₹300, MP = ₹500, desired profit = 25%. Kitna % discount de?

Step 1: Required SP
SP = 300 × 1.25 = ₹375

Step 2: Discount%
Discount% = [(MP - SP)/MP] × 100
= [(500 - 375)/500] × 100
= (125/500) × 100 = 25% ✓

Special Discount Tricks

Trick 1: Common Successive Discounts (याद कर लो!)

Commonly Asked:
10% + 10% = 19%
10% + 20% = 28%
20% + 20% = 36%
25% + 25% = 43.75%
30% + 30% = 51%
20% + 10% = 28%
15% + 15% = 27.75%

Trick 2: MP from CP and Profit% after Discount

Agar CP se x% markup aur y% discount pe z% profit chahiye:
Check: (100 + x)(100 - y)/100 = 100 + z

Example:
40% markup, 20% discount. Net profit%?
= (140 × 80)/100 - 100
= 112 - 100 = 12% profit ✓

SSC CGL Level Practice Questions

Q1. MP ₹1500 pe 30% discount. SP kya hoga?
(A) ₹1000
(B) ₹1050
(C) ₹1100
(D) ₹1150

Answer: (B) ₹1050
Solution:
SP = 1500 × 0.7 = ₹1050 ✓

Q2. Successive discounts 20% aur 15%. Single equivalent discount?
(A) 30%
(B) 32%
(C) 35%
(D) 38%

Answer: (B) 32%
Solution:
= 20 + 15 - (20×15)/100
= 35 - 3 = 32% ✓

Q3. CP = ₹600, MP = ₹900, Discount = 20%. Profit% kya hai?
(A) 15%
(B) 18%
(C) 20%
(D) 25%

Answer: (C) 20%
Solution:
SP = 900 × 0.8 = ₹720
Profit = 720 - 600 = ₹120
Profit% = (120/600) × 100 = 20% ✓

Q4. SP = ₹680, Discount = 15%. MP kya thi?
(A) ₹750
(B) ₹780
(C) ₹800
(D) ₹850

Answer: (C) ₹800
Solution:
MP = (680 × 100)/(100 - 15)
MP = 68000/85 = ₹800 ✓

Q5. Shopkeeper CP se 50% upar MP mark karta hai aur 20% discount deta hai. Profit%?
(A) 18%
(B) 20%
(C) 24%
(D) 30%

Answer: (B) 20%
Solution:
Let CP = 100
MP = 150 (50% markup)
SP = 150 × 0.8 = 120
Profit = 20, Profit% = 20% ✓

Exam Shortcuts & Quick Tricks

🚀 Trick 1: 10% Discount Quick
10% discount = Simply multiply by 0.9
Example: ₹500 pe 10% discount = 500 × 0.9 = ₹450

🚀 Trick 2: 20% Discount
20% discount = Multiply by 0.8 (or 4/5)
Example: ₹1000 pe 20% = 1000 × 4/5 = ₹800

🚀 Trick 3: 25% Discount
25% = 1/4, so 75% remains
Multiply by 3/4 directly
Example: ₹800 pe 25% = 800 × 3/4 = ₹600

🚀 Trick 4: Successive Discount Mental Math
Two equal discounts x% + x%:
Equivalent = 2x - (x²/100)
Example: 20% + 20% = 40 - 4 = 36%

Common Mistakes (ये गलतियां मत करना)

❌ Mistake 1: Successive discounts simply add करना
Wrong: 20% + 10% = 30% ✗
Right: Formula use करो = 28% ✓

❌ Mistake 2: Discount% का base CP मानना
Wrong: Discount is on CP ✗
Right: Discount हमेशा MP पर होता है ✓

❌ Mistake 3: Markup और Discount confuse करना
Markup = CP से MP तक (increase)
Discount = MP से SP तक (decrease)

❌ Mistake 4: Profit% calculation में base galat
Profit% हमेशा CP पर calculate होता है, MP पर नहीं!

Homework Practice (खुद Try करो)

MP = ₹2400 पे 35% discount. SP निकालो
Successive discounts 25% और 16%. Single equivalent?
CP = ₹800, 50% markup, 25% discount. Final profit% क्या है?
SP = ₹850, Discount = 15%. Original MP क्या थी?
Teen successive discounts 10%, 15%, 20%. Total equivalent discount?

Next Topic Preview

📚 अगले Post में: 2.5 Simple Interest (साधारण ब्याज)
SI formulas, principal-interest calculations, time-rate problems और SSC level questions!

Banking और finance से related important topic!

Conclusion

Discount SSC CGL में direct questions के साथ-साथ profit-loss problems में भी use होता है। Successive discount का formula याद कर लो - हर exam में काम आएगा। Markup + Discount combination वाले questions practice करो!

Practice Strategy: Daily 15-20 discount problems solve करो। MP, CP, SP के relationships clear रखो। Successive discounts के common values याद कर लो instant calculation के लिए!

✅ Post Complete!
Chapter 2: Arithmetic - 4/20 done (20%)
Total Progress: 16/76 posts complete (21%)
Next: 2.5 Simple Interest 🎯

Profit and Loss for SSC CGL - Complete Guide | CP, SP, Profit%, Loss%, Discount in Hindi

Learn Math • ⏱ 3 min read

📌 Series Info: Chapter 2: Arithmetic
Post Number: 15/76 | Topic: 2.3 Profit & Loss
Previous: 2.2 Percentage ✅
Chapter 2 Progress: 3/20 topics

Introduction: Profit & Loss Kya Hai?

Namaste dosto! Aaj ham Profit & Loss (लाभ और हानि) padhenge. Ye SSC CGL me guaranteed 2-3 questions aate hain aur percentage ke concepts pe based hai.

Basic Terminology

🔹 Cost Price (CP) = क्रय मूल्य = Jis price pe kharida
🔹 Selling Price (SP) = विक्रय मूल्य = Jis price pe becha
🔹 Profit = लाभ = SP > CP (when you earn)
🔹 Loss = हानि = SP < CP (when you lose)

Example 1 (Profit):
Ek pen ₹50 me khareeda, ₹60 me becha
CP = ₹50, SP = ₹60
SP > CP, toh Profit hua
Profit = SP - CP = 60 - 50 = ₹10 ✓

Example 2 (Loss):
Ek book ₹100 me khareedi, ₹80 me bechi
CP = ₹100, SP = ₹80
SP < CP, toh Loss hua
Loss = CP - SP = 100 - 80 = ₹20 ✓

🎯 Exam Importance: SSC CGL me profit-loss questions:

Direct CP/SP calculations (2-3 questions)
Profit%/Loss% based problems
Marked Price & Discount combinations
Successive discounts
False weight/dishonest dealer problems
Partnership profit distribution

Basic Profit & Loss Formulas MUST KNOW

Profit Formulas

⭐ Profit = SP - CP ⭐
⭐ Profit% = (Profit/CP) × 100 ⭐
⭐ Profit% = [(SP - CP)/CP] × 100 ⭐

Example:
CP = ₹500, SP = ₹600
Profit = 600 - 500 = ₹100
Profit% = (100/500) × 100 = 20% ✓

Loss Formulas

⭐ Loss = CP - SP ⭐
⭐ Loss% = (Loss/CP) × 100 ⭐
⭐ Loss% = [(CP - SP)/CP] × 100 ⭐

Example:
CP = ₹800, SP = ₹720
Loss = 800 - 720 = ₹80
Loss% = (80/800) × 100 = 10% ✓

SP aur CP Find Karne Ke Formulas

When Profit% Given

SP nikalna: SP = CP × [(100 + Profit%)/100]
CP nikalna: CP = [SP × 100]/(100 + Profit%)

Example 1: CP = ₹400, Profit% = 25%. SP kya hoga?
SP = 400 × [(100 + 25)/100]
SP = 400 × 1.25 = ₹500 ✓

Example 2: SP = ₹1200, Profit% = 20%. CP kya thi?
CP = (1200 × 100)/(100 + 20)
CP = 120000/120 = ₹1000 ✓

When Loss% Given

SP nikalna: SP = CP × [(100 - Loss%)/100]
CP nikalna: CP = [SP × 100]/(100 - Loss%)

Example 1: CP = ₹600, Loss% = 10%. SP kya hoga?
SP = 600 × [(100 - 10)/100]
SP = 600 × 0.9 = ₹540 ✓

Example 2: SP = ₹450, Loss% = 10%. CP kya thi?
CP = (450 × 100)/(100 - 10)
CP = 45000/90 = ₹500 ✓

Marked Price & Discount IMPORTANT

Terminology

🔹 Marked Price (MP) = अंकित मूल्य = Price tag pe likha price
🔹 Discount = छूट = MP se kitna kam
🔹 Selling Price (SP) = MP - Discount

Discount Formulas

⭐ Discount = MP - SP ⭐
⭐ Discount% = (Discount/MP) × 100 ⭐
⭐ SP = MP × [(100 - Discount%)/100] ⭐

Example:
MP = ₹1000, Discount = 20%. SP kya hoga?
SP = 1000 × [(100 - 20)/100]
SP = 1000 × 0.8 = ₹800 ✓

Combined: MP, Discount, CP, Profit

Example:
Ek shopkeeper ne article ₹500 me khareeda. Usne MP ₹800 rakha aur 10% discount diya. Profit% kya hai?

Step 1: SP nikalo
SP = 800 × 0.9 = ₹720

Step 2: Profit nikalo
Profit = SP - CP = 720 - 500 = ₹220

Step 3: Profit%
Profit% = (220/500) × 100 = 44% ✓

Successive Discounts (क्रमागत छूट)

⭐ Agar do successive discounts x% aur y% hain:
Single Equivalent Discount = x + y - (xy/100) ⭐

Example 1:
MP = ₹2000 pe pehle 20% discount, phir 10% discount. Final SP?

Method 1 (Formula):
Equivalent discount = 20 + 10 - (20×10)/100
= 30 - 2 = 28%
SP = 2000 × 0.72 = ₹1440 ✓

Method 2 (Step by step):
After 1st discount: 2000 × 0.8 = ₹1600
After 2nd discount: 1600 × 0.9 = ₹1440 ✓

Example 2:
Teen successive discounts 10%, 20%, 30%. Single equivalent discount?

Step 1: Pehle do combine karo
10 + 20 - (10×20)/100 = 28%

Step 2: Ab 28% aur 30% combine
28 + 30 - (28×30)/100
= 58 - 8.4 = 49.6% ✓

Special Cases & Tricky Problems

Case 1: Equal Profit% aur Loss%

Important Rule:
Agar do items ko same % pe ek profit aur ek loss pe becha jaye:
Overall hamesha Loss hoti hai!
Loss% = (Common %)²/100

Example:
Do articles ko ₹500 each pe becha. Ek pe 20% profit, dusre pe 20% loss. Overall profit/loss?

Quick Formula:
Loss% = (20)²/100 = 400/100 = 4% loss ✓

Verification:
Article 1: SP = 500, Profit 20% → CP = 500/1.2 = ₹416.67
Article 2: SP = 500, Loss 20% → CP = 500/0.8 = ₹625
Total CP = 416.67 + 625 = ₹1041.67
Total SP = 500 + 500 = ₹1000
Loss = 1041.67 - 1000 = ₹41.67
Loss% = (41.67/1041.67) × 100 ≈ 4% ✓

Case 2: False Weight/Dishonest Dealer

Agar dealer 1000g ke bajaye x grams deta hai:
Profit% = [(1000 - x)/x] × 100

Example:
Ek shopkeeper 1 kg ke bajaye 900g deta hai but 1 kg ka price leta hai. Uski profit%?

Profit% = [(1000 - 900)/900] × 100
= (100/900) × 100
= 11.11% ✓

Case 3: Break-even (No Profit No Loss)

Jab SP = CP, toh no profit no loss
Profit% = 0%, Loss% = 0%

Quick Reference Formulas Table

Situation	Formula
Profit	SP - CP
Loss	CP - SP
Profit%	(Profit/CP) × 100
Loss%	(Loss/CP) × 100
SP (when Profit%)	CP × [(100 + P%)/100]
SP (when Loss%)	CP × [(100 - L%)/100]
CP (when Profit%)	[SP × 100]/(100 + P%)
CP (when Loss%)	[SP × 100]/(100 - L%)
Discount	MP - SP
SP (after discount)	MP × [(100 - D%)/100]
Successive Discount	x + y - (xy/100)

SSC CGL Level Practice Questions

Q1. Ek article ₹750 me khareeda aur ₹900 me becha. Profit% kya hai?
(A) 15%
(B) 18%
(C) 20%
(D) 25%

Answer: (C) 20%
Solution:
Profit = 900 - 750 = ₹150
Profit% = (150/750) × 100 = 20% ✓

Q2. Agar CP = ₹600 aur 25% profit chahiye, toh SP kya hona chahiye?
(A) ₹700
(B) ₹725
(C) ₹750
(D) ₹800

Answer: (C) ₹750
Solution:
SP = 600 × [(100 + 25)/100]
SP = 600 × 1.25 = ₹750 ✓

Q3. MP ₹2000 pe 20% aur 10% successive discounts. Final SP?
(A) ₹1400
(B) ₹1420
(C) ₹1440
(D) ₹1460

Answer: (C) ₹1440
Solution:
Equivalent discount = 20 + 10 - (20×10)/100 = 28%
SP = 2000 × 0.72 = ₹1440 ✓

Q4. Do items ko ₹1000 each pe becha. Ek pe 25% profit, dusre pe 25% loss. Overall profit/loss?
(A) No profit no loss
(B) 6.25% profit
(C) 6.25% loss
(D) 5% loss

Answer: (C) 6.25% loss
Solution:
Loss% = (25)²/100 = 625/100 = 6.25% ✓

Q5. Ek dealer 1kg ke bajaye 800g deta hai. Uski profit% kya hai?
(A) 20%
(B) 25%
(C) 30%
(D) 33.33%

Answer: (B) 25%
Solution:
Profit% = [(1000 - 800)/800] × 100
= (200/800) × 100 = 25% ✓

Exam Shortcuts & Quick Tricks

🚀 Trick 1: 10% Profit/Loss Quick
10% profit: SP = CP × 1.1 (multiply by 11, divide by 10)
10% loss: SP = CP × 0.9 (multiply by 9, divide by 10)

🚀 Trick 2: 20% Profit Quick
20% = 1/5
CP = 5 parts → SP = 6 parts
Example: CP = ₹500 → SP = ₹600

🚀 Trick 3: 25% Profit/Loss
25% = 1/4
Profit: CP = 4 parts → SP = 5 parts
Loss: CP = 4 parts → SP = 3 parts

🚀 Trick 4: Successive Discount Mental
10% + 10% = 19% (not 20%!)
20% + 20% = 36% (not 40%!)
25% + 25% = 43.75% (not 50%!)

Common Mistakes (ये गलतियां मत करना)

❌ Mistake 1: Profit/Loss% का base confuse करना
Wrong: SP के basis पर calculate करना ✗
Right: हमेशा CP के basis पर ✓

❌ Mistake 2: Successive discounts simply add करना
Wrong: 20% + 10% = 30% ✗
Right: Formula use करो = 28% ✓

❌ Mistake 3: Equal % profit aur loss = no profit no loss
Wrong: 20% profit + 20% loss = zero ✗
Right: Overall loss hoti hai = 4% ✓

❌ Mistake 4: Discount को CP मानना
Discount हमेशा MP से होता है, CP से नहीं!

Homework Practice (खुद Try करो)

CP = ₹850, SP = ₹1020. Profit% निकालो
Loss% = 15%, SP = ₹680. CP क्या थी?
MP = ₹1500 पे 25% discount. SP क्या होगी?
Successive discounts 30% और 20%. Single equivalent discount?
दो items ₹2400 each पे बेचे। एक पे 20% profit, दूसरे पे 20% loss। Overall profit/loss%?

Next Topic Preview

📚 अगले Post में: 2.4 Discount (छूट)
Advanced discount problems, markup price, profit after discount, multiple discount combinations और SSC level questions!

आज के profit-loss concepts directly apply होंगे!

Conclusion

Profit & Loss SSC CGL का high-scoring topic है। Formulas याद करो और practice करो। CP, SP, MP का confusion clear रखो। Percentage के साथ मिलकर ये topic हर paper में आता है!

Practice Strategy: Daily 20-25 profit-loss questions solve करो। Different types practice करो - basic calculations, successive discounts, dishonest dealer problems। Speed और accuracy दोनों improve करनी है!

✅ Post Complete!
Chapter 2: Arithmetic - 3/20 done (15%)
Total Progress: 15/76 posts complete (19.7%)
Next: 2.4 Discount 🎯

Percentage for SSC CGL - Complete Guide | Formulas, Tricks & Shortcuts in Hindi

Learn Math • ⏱ 3 min read

📌 Series Info: Chapter 2: Arithmetic
Post Number: 14/76 | Topic: 2.2 Percentage
Previous: 2.1 Ratio & Proportion ✅
Chapter 2 Progress: 2/20 topics

Introduction: Percentage Kya Hai?

Namaste dosto! Aaj ham Percentage (प्रतिशत) padhenge - ye SSC CGL ka sabse important aur high-scoring topic hai. Almost har question me percentage concept use hota hai!

🔹 Percentage = "Per Cent" matlab "Per Hundred" (प्रति सौ)
Symbol: %
x% = x/100

Examples:
50% = 50/100 = 1/2 = 0.5
25% = 25/100 = 1/4 = 0.25
75% = 75/100 = 3/4 = 0.75
100% = 100/100 = 1 (complete/whole)

🎯 Exam Importance: SSC CGL me percentage directly ya indirectly har topic me:

Direct percentage calculations (2-3 questions)
Profit & Loss (percentage form me)
Discount problems
Simple & Compound Interest
Data Interpretation (graphs/charts)
Population increase/decrease

Basic Conversions (ये याद रखो!)

Fraction to Percentage

Fraction × 100 = Percentage

Example 1: 3/4 ko percentage me convert karo
= (3/4) × 100 = 75% ✓

Example 2: 5/8 = ?
= (5/8) × 100 = 62.5% ✓

Percentage to Fraction

x% = x/100 (simplify karo)

Example 1: 40% ko fraction me convert karo
= 40/100 = 2/5 ✓

Example 2: 12.5% = ?
= 12.5/100 = 125/1000 = 1/8 ✓

Decimal to Percentage

Decimal × 100 = Percentage

Examples:
0.5 = 50%
0.75 = 75%
1.25 = 125%

Common Fractions & Percentages (याद कर लो!) MUST KNOW

Fraction	Percentage	Fraction	Percentage
1/2	50%	1/11	9.09%
1/3	33.33%	1/12	8.33%
2/3	66.67%	1/13	7.69%
1/4	25%	1/15	6.67%
3/4	75%	1/16	6.25%
1/5	20%	1/20	5%
2/5	40%	1/25	4%
3/5	60%	1/50	2%
4/5	80%	1/100	1%
1/6	16.67%	3/8	37.5%
5/6	83.33%	5/8	62.5%
1/7	14.29%	7/8	87.5%
1/8	12.5%	1/9	11.11%
1/10	10%	2/9	22.22%

Percentage Calculations - Basic Formulas

Formula 1: x का y% nikalna

⭐ x का y% = (x × y)/100 ⭐

Example 1: 500 का 20% kya hai?
= (500 × 20)/100 = 100 ✓

Example 2: 1200 का 15% = ?
= (1200 × 15)/100 = 180 ✓

Formula 2: x, y का kitna % hai?

⭐ Percentage = (x/y) × 100 ⭐

Example 1: 25, 200 का kitna % hai?
= (25/200) × 100 = 12.5% ✓

Example 2: 45, 180 का kitna % hai?
= (45/180) × 100 = 25% ✓

Formula 3: Original value nikalna (percentage diya ho)

Agar x, kisi number ka y% hai, toh original number = (x × 100)/y

Example: 60 kisi number ka 15% hai. Original number kya hai?
= (60 × 100)/15 = 400 ✓
Verification: 400 का 15% = 60 ✓

Percentage Increase/Decrease VERY IMPORTANT

Percentage Increase

⭐ % Increase = [(New Value - Original Value)/Original Value] × 100 ⭐

Example: Salary ₹20,000 se badh kar ₹25,000 ho gayi. % increase?
Increase = 25000 - 20000 = 5000
% Increase = (5000/20000) × 100 = 25% ✓

Percentage Decrease

⭐ % Decrease = [(Original Value - New Value)/Original Value] × 100 ⭐

Example: Price ₹500 se kam ho kar ₹400 ho gayi. % decrease?
Decrease = 500 - 400 = 100
% Decrease = (100/500) × 100 = 20% ✓

Important Trick: Value find karna after % change

After x% increase: New Value = Original × (100 + x)/100
After x% decrease: New Value = Original × (100 - x)/100

Example 1: 800 me 25% increase ke baad value?
= 800 × (100 + 25)/100 = 800 × 1.25 = 1000 ✓

Example 2: 1200 me 20% decrease ke baad?
= 1200 × (100 - 20)/100 = 1200 × 0.8 = 960 ✓

Successive Percentage Changes (बहुत Important!) HIGH WEIGHTAGE

⭐ Agar do successive changes x% aur y% hain, toh:
Net % change = x + y + (xy/100) ⭐

• Increase ke liye: +x, +y
• Decrease ke liye: -x, -y

Example 1: Price me pehle 10% increase, phir 20% increase. Net % change?

x = +10, y = +20
Net = 10 + 20 + (10×20)/100
= 10 + 20 + 2
= 32% increase ✓

Example 2: Population pehle 20% increase, phir 10% decrease. Net change?

x = +20, y = -10
Net = 20 + (-10) + (20×(-10))/100
= 20 - 10 - 2
= 8% increase ✓

Example 3: Price pehle 25% decrease, phir 25% increase. Final price original se kitna %?

x = -25, y = +25
Net = -25 + 25 + (-25×25)/100
= 0 - 6.25
= -6.25% (means 6.25% decrease from original) ✓

Note: Equal % increase aur decrease se original value nahi milti!

Special Cases & Tricks

Case 1: Population/Value After Years

Final Value = Initial Value × [(100 ± r)/100]ⁿ
(n = number of years, r = rate %, ± depends on increase/decrease)

Example: Present population 10,000 hai. Agar har saal 5% badhta hai, toh 2 years baad?

= 10000 × [(100 + 5)/100]²
= 10000 × (1.05)²
= 10000 × 1.1025
= 11,025 ✓

Case 2: Reverse Percentage

Agar x% increase ko neutralize karna ho:
% decrease required = [x/(100 + x)] × 100

Agar x% decrease ko neutralize karna ho:
% increase required = [x/(100 - x)] × 100

Example 1: Price 25% badh gayi. Kitna % kam karo taaki original price mile?

= [25/(100 + 25)] × 100
= (25/125) × 100
= 20% ✓

Verification: Original = 100, After 25% increase = 125
125 me 20% decrease = 125 × 0.8 = 100 ✓

Example 2: Salary 20% kam ho gayi. Kitna % badhana hoga original tak laane ke liye?

= [20/(100 - 20)] × 100
= (20/80) × 100
= 25% ✓

Case 3: Percentage Point Difference

Important: "% increase" aur "percentage point increase" different hain!

Example: Marks 40% se 50% ho gaye
• Percentage point increase = 50 - 40 = 10 points
• % increase in marks = [(50-40)/40] × 100 = 25%

SSC CGL Level Practice Questions

Q1. 650 ka 15% kitna hai?
(A) 87.5
(B) 97.5
(C) 107.5
(D) 117.5

Answer: (B) 97.5
Solution:
= (650 × 15)/100 = 97.5 ✓

Q2. 45 kisi number ka 18% hai. Wo number kya hai?
(A) 200
(B) 225
(C) 250
(D) 275

Answer: (C) 250
Solution:
Number = (45 × 100)/18 = 250 ✓

Q3. Ek number pehle 20% badhta hai, phir 20% kam hota hai. Net % change?
(A) 0% (no change)
(B) 2% decrease
(C) 4% decrease
(D) 4% increase

Answer: (C) 4% decrease
Solution:
x = +20, y = -20
Net = 20 + (-20) + (20×(-20))/100
= 0 - 4 = -4% (4% decrease) ✓

Q4. Price 40% badh gayi hai. Kitna % kam karna hoga taaki original price mile?
(A) 28.57%
(B) 30%
(C) 33.33%
(D) 40%

Answer: (A) 28.57%
Solution:
= [40/(100 + 40)] × 100
= (40/140) × 100
= 28.57% ✓

Q5. Present population 8000 hai. Agar 10% per year badhta hai, toh 2 years baad kitna hoga?
(A) 9600
(B) 9680
(C) 9800
(D) 10000

Answer: (B) 9680
Solution:
= 8000 × (1.1)²
= 8000 × 1.21
= 9680 ✓

Exam Shortcuts & Quick Tricks

🚀 Trick 1: 10% Quick Calculation
10% = Simply divide by 10
Example: 450 का 10% = 45 (decimal shift!)

🚀 Trick 2: 5% Quick Method
5% = Half of 10%
Example: 600 का 5% = 30 (600 का 10% = 60, half = 30)

🚀 Trick 3: 50%, 25%, 20% Shortcuts
50% = ÷ 2
25% = ÷ 4
20% = ÷ 5
Instant calculation!

🚀 Trick 4: Fraction Approach
Percentage को fraction में convert करो, calculation fast होगा:
75% = 3/4
33.33% = 1/3
12.5% = 1/8

Common Mistakes (ये गलतियां मत करना)

❌ Mistake 1: Successive percentage में simple addition
Wrong: 10% + 20% = 30% ✗
Right: Formula use करो = 32% ✓

❌ Mistake 2: % increase और % decrease equal होने पर original value
Wrong: 25% increase then 25% decrease = original ✗
Right: Net change hoga (6.25% decrease) ✓

❌ Mistake 3: Base value confuse करना
% change हमेशा ORIGINAL value के basis पर!
Not on new value (unless specified)

Homework Practice (खुद Try करो)

750 का 18% निकालो
36 किसी number का 12% है। Original number क्या है?
Price पहले 30% बढ़ी, फिर 10% कम हुई। Net % change?
Salary 50% बढ़ गई। Kitna % कम करना होगा original तक लाने के लिए?
6000 population 15% per year बढ़ता है। 2 years बाद?

Next Topic Preview

📚 अगले Post में: 2.3 Profit & Loss (लाभ और हानि)
CP, SP, profit%, loss%, marked price, discount combinations और SSC level questions!

Profit & Loss में percentage का heavy use होता है - today's concepts directly apply होंगे!

Conclusion

Percentage SSC CGL की जान है! हर topic में percentage use होता है - Profit-Loss, SI, CI, Discount, Data Interpretation सब में। आज के formulas और tricks याद कर लो, हर question आसान हो जाएगा!

Practice Strategy: Daily 20-25 percentage questions solve करो। Different types practice करो - basic calculations, successive changes, population problems। Speed और accuracy दोनों improve करनी है!

✅ Post Complete!
Chapter 2: Arithmetic - 2/20 done
Total Progress: 14/76 posts complete (18.4%)
Next: 2.3 Profit & Loss 🎯

Ratio and Proportion for SSC CGL - Complete Guide | Formulas & Tricks in Hindi

Learn Math • ⏱ 3 min read

🎉 NEW CHAPTER START!
📌 Chapter 2: Arithmetic (Highest Weightage Chapter!)
Post Number: 13/76 | Topic: 2.1 Ratio & Proportion
Chapter 1 (Number System): Complete ✅
Chapter 2 Progress: 1/20 topics

Introduction: Ratio Aur Proportion Kya Hain?

Namaste dosto! Aaj se ham Chapter 2: Arithmetic start kar rahe hain. Ye SSC CGL ka sabse high-weightage chapter hai! Pehla topic hai Ratio & Proportion (अनुपात और समानुपात).

Ratio Kya Hai?

🔹 Ratio = Do ya zyada quantities ke beech ka comparison
Form: a : b (read as "a to b" or "a is to b")
Ya: a/b (fraction form)

Examples:
Agar ek class me 20 boys aur 15 girls hain:
Boys : Girls = 20 : 15 = 4 : 3 (simplified)

Agar ek mixture me milk aur water 3:2 me hai:
5 litre mixture me milk = 3 parts, water = 2 parts
Milk = 3 litre, Water = 2 litre

Proportion Kya Hai?

🔹 Proportion = Jab do ratios equal hote hain
Form: a : b = c : d (ya a/b = c/d)
Read as: "a is to b as c is to d"

Example:
2 : 3 = 4 : 6 (proportion hai)
Kyunki 2/3 = 4/6 (both equal to 0.666...)

🎯 Exam Importance: SSC CGL me har paper me ratio-proportion ke 3-5 questions:

Direct ratio calculations
Ratio distribution problems
Proportion finding (missing terms)
Age ratio problems
Mixture problems (ratio based)
Partnership (ratio me investment)

Ratio - Basic Concepts

Key Terminology

Ratio a : b me:
• a = First term / Antecedent (पूर्व पद)
• b = Second term / Consequent (उत्तर पद)
• a aur b dono ko terms of ratio kehte hain

Important Points

1. Unit Same Hona Chahiye
Ratio sirf same units wali quantities ka ho sakta hai
✓ Correct: 2 meters : 5 meters = 2 : 5
✗ Wrong: 2 meters : 5 cm (pehle convert karo!)

2. Ratio Unitless Hai
Ratio ka koi unit nahi hota. Ye pure number hai.
2 kg : 5 kg = 2 : 5 (units cancel out)

3. Order Matter Karta Hai
2 : 3 ≠ 3 : 2
Pehla kaun, dusra kaun – ye important hai!

Properties of Ratio

Property 1: Multiplication/Division

Dono terms ko same number se multiply/divide karne par ratio same rahta hai
a : b = ka : kb = (a/k) : (b/k)

Example:
4 : 6 ko simplify karo
Dono ko 2 se divide: 4÷2 : 6÷2 = 2 : 3 ✓

2 : 3 ko multiply by 5: 10 : 15 (same ratio) ✓

Property 2: Compound Ratio

(a : b) aur (c : d) ka compound ratio = ac : bd

Example:
(2 : 3) aur (4 : 5) ka compound ratio?
= (2×4) : (3×5) = 8 : 15 ✓

Property 3: Duplicate Ratio

a : b ka duplicate ratio = a² : b²

Example:
3 : 4 ka duplicate ratio = 9 : 16 ✓

Property 4: Sub-duplicate Ratio

a : b ka sub-duplicate ratio = √a : √b

Example:
9 : 16 ka sub-duplicate ratio = 3 : 4 ✓

Property 5: Triplicate Ratio

a : b ka triplicate ratio = a³ : b³

Example:
2 : 3 ka triplicate ratio = 8 : 27 ✓

Property 6: Inverse/Reciprocal Ratio

a : b ka inverse ratio = b : a (ya 1/a : 1/b)

Example:
3 : 5 ka inverse = 5 : 3 ✓

Proportion - Complete Concepts

Basic Definition

⭐ a : b :: c : d (ya a : b = c : d)
Matlab: a/b = c/d
Cross multiplication: a × d = b × c ⭐

Example:
Check karo: 3 : 5 :: 6 : 10 proportion hai ya nahi?
Cross multiply: 3 × 10 = 30
5 × 6 = 30
30 = 30, toh YES, proportion hai! ✓

Terminology in Proportion

a : b :: c : d me:
• a, d = Extremes (बाह्य पद)
• b, c = Means (मध्य पद)

Rule: Product of extremes = Product of means
a × d = b × c

Types of Proportion

1. Continued Proportion

Teen quantities a, b, c continued proportion me hain agar:
a : b :: b : c
Ya: a/b = b/c
Matlab: b² = ac

b ko mean proportional kehte hain

Example:
2, 4, 8 continued proportion me hain?
Check: 4² = 16, aur 2 × 8 = 16 ✓
Yes! 2 : 4 :: 4 : 8

Example 2:
3 aur 12 ke beech mean proportional kya hoga?
b² = 3 × 12 = 36
b = 6 ✓
Toh 3, 6, 12 continued proportion me hain

2. Third Proportional

Agar a : b :: b : c, toh c ko third proportional kehte hain
Formula: c = b²/a

Example:
4 aur 8 ka third proportional nikalo
c = 8²/4 = 64/4 = 16 ✓
Verify: 4 : 8 :: 8 : 16 (4×16 = 8×8 = 64)

3. Fourth Proportional

Agar a : b :: c : d, toh d ko fourth proportional kehte hain
Formula: d = bc/a

Example:
2, 3, 4 ka fourth proportional?
d = (3×4)/2 = 12/2 = 6 ✓
Verify: 2 : 3 :: 4 : 6 (2×6 = 3×4 = 12)

Componendo & Dividendo IMPORTANT

Agar a/b = c/d, toh:

Componendo

(a + b)/b = (c + d)/d

Dividendo

(a - b)/b = (c - d)/d

Componendo & Dividendo (Combined)

⭐ (a + b)/(a - b) = (c + d)/(c - d) ⭐
Ye bahut useful hai complex problems me!

Example:
Agar x/y = 3/4, toh (x+y)/(x-y) ka value?

Componendo-Dividendo use karo:
(x+y)/(x-y) = (3+4)/(3-4) = 7/(-1) = -7 ✓

Ratio Distribution Problems

Method:
1. Total amount = Sum of all parts
2. Each share = (Ratio part / Sum of ratios) × Total

Example 1:
₹5000 ko A, B, C me 2:3:5 ke ratio me divide karo

Step 1: Sum of ratios = 2 + 3 + 5 = 10
Step 2:
A ka share = (2/10) × 5000 = ₹1000
B ka share = (3/10) × 5000 = ₹1500
C ka share = (5/10) × 5000 = ₹2500

Verification: 1000 + 1500 + 2500 = 5000 ✓

Example 2:
Teen numbers ka ratio 3:4:7 hai aur unka sum 420 hai. Sabse bada number kya hai?

Sum of ratios = 3 + 4 + 7 = 14
Sabse bada number (7 parts) = (7/14) × 420 = 210 ✓

Age-Based Ratio Problems

Example:
A aur B ki present ages ka ratio 4:5 hai. 6 years baad unki ages ka ratio 5:6 ho jayega. Unki present ages kya hain?

Solution:
Let present ages: A = 4x, B = 5x

6 years baad:
(4x + 6)/(5x + 6) = 5/6

Cross multiply:
6(4x + 6) = 5(5x + 6)
24x + 36 = 25x + 30
x = 6

A's age = 4 × 6 = 24 years ✓
B's age = 5 × 6 = 30 years ✓

SSC CGL Level Practice Questions

Q1. Agar A:B = 2:3 aur B:C = 4:5, toh A:B:C ka ratio kya hoga?
(A) 2:3:5
(B) 8:12:15
(C) 2:4:5
(D) 8:12:20

Answer: (B) 8:12:15
Solution:
A:B = 2:3
B:C = 4:5

B ko equal banao (LCM of 3 and 4 = 12):
A:B = 2:3 = 8:12 (multiply by 4)
B:C = 4:5 = 12:15 (multiply by 3)

A:B:C = 8:12:15 ✓

Q2. ₹680 ko A, B, C me 2:3:12 ke ratio me baantne par A ko kitne rupaye milenge?
(A) ₹60
(B) ₹80
(C) ₹100
(D) ₹120

Answer: (B) ₹80
Solution:
Sum = 2 + 3 + 12 = 17
A's share = (2/17) × 680 = 80 ✓

Q3. 12 aur 48 ka third proportional kya hoga?
(A) 96
(B) 144
(C) 192
(D) 240

Answer: (C) 192
Solution:
c = b²/a = 48²/12 = 2304/12 = 192 ✓

Q4. Agar x:y = 3:4, toh (x² + y²):(x² - y²) ka value?
(A) 25:7
(B) 7:25
(C) 25:-7
(D) -7:25

Answer: (C) 25:-7
Solution:
Let x = 3k, y = 4k
x² + y² = 9k² + 16k² = 25k²
x² - y² = 9k² - 16k² = -7k²
Ratio = 25k²:(-7k²) = 25:-7 ✓

Q5. 18 aur 32 ka mean proportional kya hai?
(A) 24
(B) 25
(C) 20
(D) 28

Answer: (A) 24
Solution:
Mean proportional = √(18 × 32) = √576 = 24 ✓

Exam Shortcuts & Tricks

🚀 Trick 1: Quick Simplification
Ratio simplify karne ke liye HCF use karo
Example: 24:36 → HCF = 12 → 2:3 ✓

🚀 Trick 2: Combined Ratio
A:B = 2:3 aur B:C = 4:5
B ko common banao (LCM method)
Fast calculation!

🚀 Trick 3: Age Problems
Present ratio aur future/past ratio dono given ho:
Equation banao aur solve karo
Always verify answer!

🚀 Trick 4: Distribution Formula
Share = (Ratio part / Sum of all parts) × Total
Ye yaad rakho, har question instant solve!

Common Mistakes (Ye Galtiyan Mat Karna)

❌ Mistake 1: Units different hone par compare karna
2 meters : 500 cm ko directly 2:500 mat likho!
Pehle same unit me convert: 200 cm : 500 cm = 2:5 ✓

❌ Mistake 2: Order reverse kar dena
Boys:Girls = 2:3 hai toh Girls:Boys = 2:3 nahi!
Correct: Girls:Boys = 3:2 ✓

❌ Mistake 3: Sum of ratios bhoolna
Distribution me total parts add karna bhool jaate hain
Always calculate sum first!

Homework Practice (Khud Try Karo)

₹1200 ko A, B, C me 3:4:5 ke ratio me divide karo. C ko kitne rupaye milenge?
Agar A:B = 3:5 aur B:C = 2:3, toh A:C kya hoga?
9 aur 36 ka third proportional kya hai?
Agar (x+y):(x-y) = 7:3, toh x:y kya hoga?
Present ages ka ratio 5:7 hai. 10 years pehle ratio 3:5 tha. Present ages nikalo.

Next Topic Preview

📚 Agle Post Me: 2.2 Percentage (प्रतिशत)
Percentage calculations, fraction to percentage conversion, percentage increase/decrease, successive percentages aur SSC level questions!

Percentage is one of the MOST important topics – har topic me use hota hai!

Conclusion

Ratio & Proportion arithmetic ka foundation hai. Ye concept clear ho gaya toh aage ke sab topics (percentage, profit-loss, mixture, partnership) easy ho jayenge!

Practice Strategy: Daily 15-20 ratio problems solve karo. Different types practice karo – distribution, age, combined ratios. Speed aur accuracy dono improve karni hai!

✅ Post Complete!
Chapter 2: Arithmetic - 1/20 done
Total Progress: 13/76 posts complete (17.1%)
Next: 2.2 Percentage 🎯