🎉 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
📌 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)
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
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"
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...)
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
• 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!)
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)
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!
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)
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) ✓
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 ✓
(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 ✓
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 ✓
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 ✓
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 ✓
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 ⭐
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! ✓
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
• 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
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
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
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
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)
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
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)
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!
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 ✓
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
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 ✓
₹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 ✓
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 ✓
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 ✓
(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 ✓
(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 ✓
(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 ✓
(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 ✓
(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 ✓
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!
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!
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!
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 ✓
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 ✓
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!
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!
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 🎯
Chapter 2: Arithmetic - 1/20 done
Total Progress: 13/76 posts complete (17.1%)
Next: 2.2 Percentage 🎯