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

📌 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
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